Engineering 
Library 


ALTERNATING   CURRENT   DESIGN 


ALTERNATING 
CURRENT    DESIGN 


BY 

JULIUS   FRITH,    M.Sc.,    M.I.E.E. 

CONSULTING  ENGINEER 

SPECIAL  LECTURER    IN   ELECTRICAL  DESIGN    IN   THE  MANCHESTER 
UNIVERSITY 


LONDON  AND  NEW  YORK 

HARPER    6f   BROTHERS 

45   ALBEMARLE   STREET,  W. 
1912 

(All  rights  reserved) 

B.  VAN  NOSTRAND  COMPANY 

K*W    YOKK 


Engineering 
Library 


PREFACE 

LET  me  say  at  once  that  this  book  does  not,  and  is 
not  meant  to,  cover  the  whole  of  the  subject  suggested 
by  its  title.  It  is  intended,  for  instance,  to  be  a 
companion  book  to  Mr.  Cramp's  "  Continuous  Current 
Machine  Design,"  to  which  treatise  the  reader  is  referred 
for  much  of  the  ground  that  would  otherwise  have 
been  twice  traversed,  as,  for  example,  the  sections  on 
Temperature  Rise  arid  Insulation,  together  with  nearly 
all  the  purely  mechanical  parts  of  design,  including 
works  costing. 

Of  the  rest,  I  have  perhaps  aimed  at  giving  that 
which  I  have  not  found  in  similar  books,  and  particularly 
have  I  aimed  at  expressing  it  in  a  non-mathematical 
way,  endeavouring  to  emphasize  the  inward  physical 
meaning  rather  than  the  outward  mathematical  form, 
to  impart  ideas  rather  than  information. 

I  hope  the  book  will  be  useful  alike  to  students 
and  to  those  engaged  in  works,  and  I  sometimes  dare 
to  hope  that  my  brother  designers  will  find  one  or  two 
things  presented  in  a  new  light  which  may  stimulate 
them  even  whilst  disagreeing. 

Of  those  to  whom  I  have  become  indebted  over 
the  compilation  of  this  book  I  shall  have  space  only 
to  mention  a  few.  My  friend  and  late  assistant, 


VI  PREFACE 

Mr.  R.  E.  Grime,  comes  easily  first,  for  from  his  notes 
I  have  largely  helped  myself  for  material  for  many  of 
the  chapters. 

The  idea  of  the  price  curves  for  cables  is  taken  from 
a  paper  by  Mr.  H.  A.  Earle,  and  the  idea  of  sodium 
as  a  conductor  from  Betts.  The  costs  of  most  of  the 
more  usual  metals  in  Chapter  XL  were  obtained  for 
me  by  Messrs.  Carrick  &  Brockbank  of  this  city,  and 
those  of  the  rarer  metals  by  Messrs.  Johnson  Matthey 
of  London. 

I  shall  at  any  time  be  pleased  to  receive,  and  if 
possible  to  answer,  letters  of  suggestion,  criticism  or 
correction. 

JULIUS  FKITH. 

THE  HOMESTEAD, 

VICTORIA  PARK,  MANCHESTER, 
November,   1911. 


CONTENTS 

CHAPTBE  I 
ALTEENATING  CURRENTS 

PAGK 

Elementary  alternator — The  production  of  an  alternating  E.M.F. 
— The  flow  of  an  alternating  current  through  circuits  having 
resistance,  self-induction,  and  capacity — Angle  of  lag  .  .  1 

CHAPTEE  II 
ARMATUEE  REACTION 

System  of  vectors  used — Various  fluxes  existing  in  an  alternator 
— Ampere  turns  to  drive  these  fluxes — Demagnetizing  ampere 
turns  on  the  stator — Numerical  values  of  fluxes  and  ampere 
turns — Inherent  regulation — Pre-determination  of  behaviour 
of  alternator  10 


CHAPTER  III 
RELATION   OF  DIMENSIONS  TO   OUTPUT 

Ampere   turns  per  inch  diameter — Induction   in  the  air  space — 

D2Z  formula — Limits  of  convenience    ......      20 


CHAPTER   IV 
EXAMPLE  OF  THE  DESIGN  OF  AN  ALTERNATOR 

Specification  for  a  250  KW.  alternator — Diameter — Stator  winding 
— "  Field  effect  " — The  magnetic  circuit — Synthesis  with  full 
load  fluxes — Magnet  winding — Open  circuit  synthesis — Rotor 
ampere  turns  at  various  loads  and  power  factors — Short 
circuit — Efficiencies — Weights  and  costs  of  active  material  .  24 


viii  CONTENTS 

OHAPTEE  V 
SYNCHEONOUS  MACHINEKY  IN   PAEALLEL 

PAGE 

Stator  flux  independent  of  rotor  excitation— Eelative  position  of 
stator  and  rotor  poles— Synchronous  motors— Cyclic  irregu- 
larity— Meaning  of  power  factor 40 

CHAPTER  VI 
COMPOUND-WOUND  ALTEENATOES 

Compounding  by  separate  windings — By  action  on  the  exciter — By 

armature  reaction  itself  46 


CHAPTEE  VII 
INDUCTION   MOTOES— THEOEY 

Importance  of  power  factor — Leakage  fields— Determination  of  <r 
— The  Heyland  Diagram — Eatio  of  no  load  to  full  load  currents 
— Ampere  turns  per  cm.  diameter 51 


CHAPTER  VIII 
EXAMPLE  OF  THE   DESIGN   OF  AN   INDUCTION   MOTOE 

Specification  for  50  B.H.P.  induction  motor — Diameter  and  number 
of  slots— Maximum  power  factor— Stator  and  rotor  windings- 
Synthesis  of  magnetization  current — Losses — Predetermination 
of  power  factor,  H.P.  slip,  and  efficiency — Weights  and  costs  of 
active  material  ..........  61 


CHAPTER   IX 
STATIC   TEANSFOEMEES 

Core  and  shell  type — Theory  of  transformers — Eesistance  and 
reactance  drop — Transformers  feeding  rotary  converters — 
Disadvantage  of  too  close  voltage  regulation — Eatio  of  flux  to 
ampere  turns — Air  and  oil  cooling — Best  depth  of  coils  .  .  71 


CONTENTS  IX 

CHAPTER   X 
EXAMPLE   OF  THE  DESIGN   OF  A  TRANSFORMER 

PAGE 

Making  of  circular  cores — Windings — Losses  and  efficiency — 
Weights  and  costs  of  active  material — Magnetizing  current — 
Voltage  regulation 81 

CHAPTER  XI 

TRANSMISSION  LINES 

Comparison  of  different  systems — Single  phase,  two  phase,  and 
three  phase — Three  phase  with  transformers — Cheapest  voltage 
—Price  curves— Best  material  for  transmitting  electricity  .  87 

CHAPTER  XII 

CHOKING  COILS 

Theory — Example — Comparison  with  resistances     ....      96 

CHAPTER    XIII 

ADDITIONAL  EXAMPLE  OF  THE  DESIGN  OF 
AN  ALTERNATOR 

Constant  pressure  and  constant  power — Design  of  a  two-phase 
furnace  alternator — Constant  power  curves — Efficiency — 
Weights  and  costs  of  active  material 99 

CHAPTER    XIV 

DESIGN  OF  A  SMALLER  TWO-PHASE  SQUIRREL-CAGE 
INDUCTION   MOTOR  AND  AUTO-STARTER 

Advantages  and  disadvantages  of  squirrel-cage  windings — Design  of 
a  5  H.P.  motor — Behaviour  of  same — Cost  of  active  material — 
Principle  of  auto -transformer  starter — Design  of  starter  for 
the  above  motor 106 


LIST    OF   SYMBOLS 
AND   CONTRACTIONS    USED 

Ap     Area  of  cable  for  a  loss  of  p  per  cent,  per  mile,  in  Chapter  XI. 
AA     Area    of    cable  for    a   density   of   A    amperes  per    in2,   in 
Chapter  XI. 

A.T.'s    Ampere  turns. 

a    Angle  between  a  coil  when  first  observed  and  its  position  of 
maximum  flux,  in  Chapter  I. 

B     Magnetic  induction  in  lines  per  cm2. 
C     R.M.S.  current  in  amperes. 
Co    Current  at  no  load,  hence  magnetizing  current  in  Induction 

Motors,  in  Chapter  VII.,  etc. 
0  C.     Degrees  Centigrade. 
C.G-.S.     Centimetre-gramme-second  units. 
C.S.     Cast  steel. 
Cu    Copper, 
cm.     Centimetre. 
cm2.,  cm3.    Square  and  cubic  centimetre. 

D    Diameter  of  stator  at  the  air  space,  injChapter  III.,  etc. 
d    Diameter  of  iron  core  of  a  transformer,  in  Chapter  IX. 
D.C.    Direct  current. 

A     Amperes  per  square  inch  in  copper. 

S    Eadial  clearance  between   stator    and    rotor    of    Induction 

Motor,  in  Chapter  VIII. 

Also  density  of  a  metal  in  grammes  per  cm3.,  in  Chapter  XI. 
E    Maximum  value  of  E.M.F.,  in  Chapter  I. 

Elsewhere  E.M.S.  value  of  E.M.F. 
er    Volts  lost  in  resistance  of  transformer  windings,  in  Chapter  IX. 


Xll       LIST  OF  SYMBOLS  AND   CONTRACTIONS    USED 

es    Volts  lost  in  reactance  of  transformer  windings,  in  Chapter  IX. 
E.M.F.    Electro-motive  force  in  volts. 

F.     Capacity  in  farads,  in  Chapter  I. 

4>     Angle  between  the  maximum  value  of  current  and  volts. 

cos  <£  =  power  factor. 
H    Magnetic  lines  of  force  per  cm2,  in  air,  in  Chapter  I. 

Elsewhere  C.G.S.  magnetizing  force  per  cm. 
H.P.     Horse-power. 
H.T.     High  tension,  in  Chapter  X. 

I    Maximum    value    of    alternating    current    in    amperes,   in 
Chapter  I. 

in.  Inches. 

in2.,  in3.  Square  and  cubic  inch. 

K  Cost  of  material  in  «£'s  per  ton,  in  Chapter  XI, 

KW.'s  Kilowatts 

K.V.A.'s  Kilo-volt-amperes. 

L  Self-induction  in  henries,  in  Chapter  I. 

I    Length  of  an  active  conductor,  gross  length  of  stator  plates, 
axial  length  of  stator. 

Also  a  length  in  cms.  of  a  magnetic  path. 

Also  the  length  of  a  limb  of  a  transformer  in  Chapter  IX. 
L.T.     Low  tension,  in  Chapter  X. 
M.S.     Mild  steel. 

mb     Function  of  increase  of  resistance  due  to  a  conductor's  own 
field,  in  Chapter  IV. 

mm.'s     Milimetres. 

N     Magnetic  flux  linking  a  coil,  or  per  pole,  in  Chapter  I.,  etc. 

Number  of  slots  per  pole  in  "cr"  formula,  in  Chapter  VII.,  etc. 
P    Phosphorus,  in  Chapter  XI. 

Also  number  of  poles. 

P.c.     Price  of  copper  per  in3.,  in  Chapter  IX. 
P.i.     Price  of  iron  per  in3.,  in  Chapter  IX. 
p     Percentage  loss  per  mile  in  cables,  in  Chapter  XI. 
p.f.    Power  factor. 
Q    Maximum  quantity  of  electricity  in  condenser,  in  Chapter  I. 


LIST  OF  SYMBOLS  AND   CONTRACTIONS    USED    xiii 
B    Eesistance  in  ohms. 

1  Revolutions  per  minute. 
r.p.m.J 

E.M.S.     Square  root  of  mean  square  of  a  sine  wave, 

Virtual  value  of  an  alternating  current  or  voltage. 
r    length  of  radial  arms  of  an  active  conductor,  in  Chapter  I. 
p    Eatio  of  primary  and  secondary  turns  on  a  transformer,  in 

Chapter  IX. 

Also  specific  resistance  in  microhms  per  cm3,  at  15°  C.,  in 
Chapter  XI. 

5  Tensile  strength  in  tons  per  in2.,  in  Chapter  XI. 
Sn    Tin. 

Si    Silicon, 
o-    1  +  o-  is  the  waste  field  coefficient   of  an  Induction  Motor, 

in  Chapter  VII.,  etc. 
T    Turns  per  phase. 

ETj  &  T2    Primary  and  secondary  turns  on  a  transformer,  in  Chapter  IX. 
t    Time  in  seconds  since  the  beginning,  in  Chapter  I. 
Also  depth  of  copper  in  transformer  coils,  in  Chapter  IX. 

6  Angle  between  the  coil  and  its  position  of  maximum  flux,  in 

Chapter  I. 

r    Pitch  of  poles,  N.  to  S.,  in  Chapter  VII. 
V    Velocity  in  cms.  per  second,  in  Chapter  I. 
W    Watts  output,  in  Chapter  IX. 
W.I.    Wrought  iron, 
w.f.c.    Waste  field  coefficient. 
Zn    Zinc,  in  Chapter  XI. 
o>     Eadians  per  second  of  elementary  alternator,  in  Chapter  I.,  etc. 

=  27T~ 

~    Eevolutions  per  second  of  elementary  alternator,  in  Chapter  I. 
Complete    reversals  per  second  of  alternating  current  and 
voltage. 


ALTERNATING    CURRENT 
DESIGN 


CHAPTER   I 

ALTERNATING    CURRENTS 

THE  simplest  form  of  alternator  possible  would  be  a 
single  conductor  supported  parallel  to  a  shaft  by  radial 
arms  and  revolved  in  a  uniform  magnetic  field.  It  is 
worth  while  to  study  such  an  arrangement  and  the 
laws  which  can  be  deduced  from  its  behaviour  before 
considering  the  more  practical  forms  of  alternating 
current  generators  (Fig.  1). 

If  the  length  of  the  conductor  parallel  to  the  shaft 
be  /  centimetres,  that  of  the  radial  arms  r  cms.,  the 
peripheral  speed  of  the  conductor  V  cms.  per  second, 
and  the  uniform  magnetic  field  H  lines  per  square 
centimetre,  then  the  maximum  electro-motive  force 
generated  in  the  conductor  will  beH.Z.Vx  10~8  volts. 
There  is  no  E.M.F.  in  the  shaft  or  in  the  radial 
supporting  arms  because  they  cut  no  lines  of  force. 

If  we  call  the  revolutions  per  second  ^  and  the 
radians  per  second  w,  then  o>  =  2^^  and  V  =  ZTTT^  =  wr. 
So  that  the  maximum  E.M.F.  E  =  H/wr  x  10~8  volts. 

i  B 


*•»       0         ?•" , 
a"  :  "jtLT£JWATlWG   CURRENT  DESIGN 

But  £  x  T  is  the  area  of  the  coil  in  cms2,  and  H  .  I .  r 
is  the  maximum  number  of  lines  of  force  ever  through 
the  coil ;  calling  these  N,  the  maximum  E.M.F. 
E  =  w.N.lO-8. 

This  is  one  of  the  most  universal  relations  in  the 
whole  of  alternating  current  work ;  whenever  lines  of 


+       //  ///?es  per  cm  * 


revo/uf/ons  per  sec 
co  rad/axs  per  second 


^ 
FIG.  l. 


force  through  a  coil  vary  from  a  maximum  N  at  the 
rate  of  ^  complete  reversals  per  second,  then  the 
maximum  E.M.F.  in  each  turn  of  that  coil  is  w  .  N .  10~8 
where  cy  =  ZTT^.  This  is  true  however  the  lines  may 
be  varied,  either  by  revolving  the  coil,  or  revolving 
the  field,  or  magnetizing  an  iron  core  which  passes 


ALTERNATING   CURRENTS  3 

through  the  coil,  or  if  the  lines  merely  link  the  coil 
due  to  current  in  the  coil  itself.  It  is  true  whether 
the  lines  of  force  cause  the  E.M.F.,  or  whether  the 
E.M.F.  in  being  applied  to  a  coil  sends  such  a  current 
through  it  as  will  magnetize  for  that  flux  N,  so  that, 
neglecting  only  the  volts  lost  in  resistance,  the  reading 
of  a  voltmeter  is  always  a  measure  of  the  flux. 

Returning  to  the  elementary  alternator,  it  is  seen 
that  at  the  instant  when  the  E.M.F.  is  a  maximum  the 
number  of  lines  of  force  threading  the  coil  is  zero  and 
vice  versd,  i.e.  that  the  maximum  of  the  lines  through 
the  coil  and  that  of  the  E.M.F.  in  the  coil  are  separated 
by  a  quarter  of  a  period,  or  90  degrees.  This  result 
is  also  true  of  all  cases,  just  as  the  former  one 
was. 

The  E.M.F.  at  any  other  position  of  the  coil  will  be 
proportional  to  that  component  of  V  which  is  at  right 
angles  to  the  field,  the  other  component  not  cutting 
lines.  This  active  component  is  V  sin  9,  where  6  is 
the  angle  between  the  coil  at  any  instant  and  the  coil 
when  the  maximum  number  of  lines  pass  through  it, 
i.e.  when  the  E.M.F.  is  zero.  At  other  times  the 
instantaneous  value  of  the  E.M.F.  is  E  sin  0.  This  is 
sometimes  written  E  sin  (a>t),  where  o>  is  the  angle  in 
radians  turned  through  per  second  and  t  is  the  number 
of  seconds  elapsed  since  the  beginning  of  movement. 
cot  is  thus  an  angle  like  6,  but  unlike  6  it  can  be  any 
number  of  whole  revolutions  plus  any  fraction  of  a 
revolution.  If  the  coil  was  not  right  across  the  lines 
at  the  beginning,  but  inclined  to  that  position  at  any 


4  ALTERNATING   CURRENT  DESIGN 

angle  a,  then  to  be  quite  accurate  the  instantaneous 
value  of  the  E.M.F.  is  written  as  E  sin  (a  -f  cot). 

For  these  reasons  the  curve  representing  the  varia- 
tion of  E.M.F.  with  time  is  called  a  "  sine  wave/'  and, 
without  entering  into  a  mathematical  discussion  of  its 
properties,  we  can  take  a  few  of  them  on  trust.  Most 
of  the  usefulness  of  electro -motive  force  for  purposes 
of  doing  work  depends  on  the  square  of  the  E.M.F.,  so 
that  if  the  E  M.F.  is  alternating,  it  is  the  square  root  of 
the  mean  square  which  is  then  required,  and  which 
is  measured  on  a  voltmeter ;  for  a  sine  wave  this 
R.M.S.  value,  as  it  is  written,  is  the  maximum  value 
divided  by  \/~%.  Sometimes,  however,  we  require  the 
simple  average  current  over  half  a  period,  and  this  is 

the  maximum  value  divided  by  -. 

2i 

It  will  be  noticed  that  in  the  foregoing  the  pro- 
duction of  an  E.M.F.  is  sometimes  attributed  to  a 
conductor  cutting  lines  of  force,  and  sometimes  to  the 
rate  of  change  of  lines  linking  the  circuit,  and  there 
are  nearly  always  these  two  ways  of  looking  at  the 
phenomenon.  In  some  cases  one  is  the  more  convenient 
method,  and  in  others  the  other,  but  oftener  the  two 
points  of  view  together  give  the  best  perspective. 

Now  let  this  E.M.F.  send  a  current  through  a 
second  coil  having  a  resistance  of  E  ohms  and  a  self- 
induction  of  L  henries,  and  let  the  maximum  value  of 
the  resulting  current  be  I  amperes.  The  current  I 
flowing  through  the  resistance  R,  will  give  rise  to  a 
vpltage  R .  I,  but  it  will  also  give  rise  to  a  number  of 


ALTERNATING   CURRENTS  5 

lines  of  force  linking  the  coil,  the  maximum  value  of 
which  will  be  L .  1 .  108,  for  L  is  by  definition  of  the  unit 
of  self-induction  the  number  of  108  lines  linking  the 
circuit  for  each  ampere  round  the  circuit.  These  lines 
give  rise  to  an  E.M.F.  of  o> .  L .  I,  which  we  have  already 
seen  will  be  90  degrees  behind  the  current.  The 
E.M.F.  K  .  I  is  in  phase  with  the  current,  that  is,  has  its 
maximum  value  at  the  same  instant  as  the  maximum 
current. 

The  value  of  the  current  will  so  adjust  itself  that 


CO. LI 


R.I 

FIG.  2. 


the  resultant  of  these   two  will   equal   the   impressed 
E.M.F.     So  that— 


E  =  \/(RI)8  +  (o)LI)2 

T  E 

=  x/R2  +  LV 

The  root  \/E2  +  L  V  is  the  impedance  of  the  circuit 
and  takes  the  place  of  the  plain  resistance  in  direct 
current  work. 

Now,  instead  of  the  circuit  having  resistance  and 
self-induction,  let  it  have  resistance  K  and  capacity  F 
farads ;  the  capacity  of  a  condenser  being  the  amount 
of  electricity  in  coulombs  required  to  charge  it  to  a 
potential  of  one  volt,  a  flow  of  one  coulomb  per  second 
being  called  an  ampere. 


6  ALTERNATING   CURRENT  DESIGN 

Let  Q  be  the  maximum  quantity  of  electricity  ever 
in  the  condenser  at  one  time.  This  will  occur  when 
the  current  has  been  flowing  in  one  direction  for  as 
long  as  possible  and  is  just  going  to  reverse,  and 
therefore  equals  zero. 

The  potential  at  the  condenser  will  then  be  a 
maximum  and  equal  to  Q  divided  by  F,  so  that  it  is 
seen  that  the  maximum  potential  is  90  degrees  from  the 
maximum  of  current. 

Q  is  the  quantity  of  electricity  that  flows  into  the 
condenser  during  one  quarter  of  a  wave,  and  as  there 

are  **  waves  per  second  the  time  taken  is  —  seconds ; 

4,-w 

the  average  current  is  therefore  4  ^  Q  amperes.  This 
average  current  is  equal  to  the  maximum  divided 

by  - ;  therefore 

2i 

I  =  ?  X  4~Q  =  27r~Q  =  «Q 

2t 

The  potential  of  the  condenser  =  ~  =  — ^.     As  before 

F       wY 

there  is  an  E.M.F.  R .  I  in  phase  with  the  current,  and  the 
resultant  of  these  two  at  right  angles  must  equal  E,  so 
that — 


or  I  = 


the  denominator  being  the  impedance  of  the  circuit. 


ALTERNATING   CURRENTS  7 

Next  consider  a  circuit  having  both  resistance,  self- 
induction,  and  capacity.  It  follows  from  the  above 
that  the  potentials  at  the  terminals  of  the  two  latter, 
being  both  at  right  angles  to  the  current,  are  themselves 
in  the  same  straight  line,  and  it  only  remains  to 
determine  if  they  are  in  the  same  or  opposite  directions. 


F.CO 


R.T. 

FIG.  3. 


Consider  the  instant  when  the  current  is  just 
reversing.  It  has  been  flowing  into  the  condenser  up 
to  now,  which  is  therefore  full,  and  on  the  current 
reversing  will  begin  to  discharge,  aiding  the  recently 
reversed  current.  The  lines  of  force  linking  the  part  of 
the  circuit  having  self-induction,  on  the  contrary,  will  be 
just  increasing  and  building  up  an  E.M.F.  in  opposition 
to  the  increasing  current. 

This  shows  that  the  two  E.M.F.'s  are  in  opposite 
directions  at  the  terminals  of  the  capacity  and  self- 
induction,  and  therefore 


which    is    the    general    expression    for    the    flow    of 
alternating  currents. 

It  is  worth  while  to  notice  that  whichever  of  the  last 
two  terms  is  the  greater,  the  bracket  is  always  positive  ; 


8  ALTERNATING   CURRENT  DESIGN 

it,   however,  vanishes  when   L&>  =  -^r ,    when    the   ex- 

JDO) 

pression  becomes  one  of  Ohm's  Law  merely.  This 
means  that  for  every  circuit  having  both  self-induction 
and  capacity  there  is  one  frequency  at  which  the  effects 
of  both  vanish  and  the  circuit  behaves  as  if  it  contained 


resistance  only.  If  a  means  exists  of  supplying  the 
circuit  with  a  variable  frequency,  this  forms  a  ready 
means  of  measuring  either  self-induction  or  capacity, 
the  value  of  the  other  being  known,  as  the  current 
suffers  an  extremely  rapid  variation  as  the  frequency 
nears  the  critical  value. 

The  foregoing  work  also  defines  the  power  factor, 
which  is  the  cosine  of  the  angle  between  the  current 
and  the  impressed  E.M.F.  The  tangent  of  this 
angle  is,  in  the  case  of  resistance  and  self-induction 

alone,     ^-=  —  ^  —  ,   so   that  the   power  factor  of  a 
K  K 

circuit  is  seen  to  decrease  as  either  the  self-induction  or 
the  frequency  increase  or  as  the  resistance  decreases. 
In  the  case  of  resistance  and  capacity 


and  the  power  factor  increases  as  either  the  frequency, 
capacity,  or  resistance  increase. 


ALTERNATING   CURRENTS 


In  the  most  general  case  of  a  circuit  containing 
resistance,  self-induction,  and  capacity, 


and  the  power  factor  will  be  either  leading  or  lagging 
according  as  ^—  is  greater  or  less  than  Lo> ;  when  these 

are  equal  the  current  will  be  in  phase  with  the  voltage, 
i.e.  the  power  factor  will  be  unity. 


CHAPTER   II 

ARMATURE    REACTION 

IN  the  last  chapter  the  effect  of  the  current  on  the 
behaviour  of  the  alternator  itself  was  neglected.  This 
is,  however,  a  very  important  matter  which  we  will  now 
consider.  For  this  purpose  a  very  simple  vector 
diagram  will  be  used.  Fixing  our  attention  for  the 
moment  on  a  two-pole  revolving  field  alternator,  let  us, 
as  it  were,  point  with  vectors  to  the  maximum  values  of 
the  current,  voltage,  fluxes,  etc.,  as  they  revolve  round 
the  centre ;  these  vectors  by  their  length  will  also,  to 
some  convenient  scales,  represent  the  magnitude  of  the 
quantities  involved. 

It  is  seen  that  this  system  of  picturing  what  is  happen- 
ing in  the  alternator  by  pointer  vectors  represents  the 
relation  between  the  various  quantities  in  space,  and  for 
this  reason  must  not  be  confused  with  any  other  system 
of  vectors  which  might  endeavour  to  represent  this 
mutual  relationship  in  time.  The  angle  whose  cosine 
we  call  the  power  factor  is  an  example  of  the  former 
notation,  in  that  it  represents  the  space  separating  the 
maximum  values  of  the  voltage  and  current ;  to 
translate  such  an  angle,  expressed  in  degrees,  into 
seconds  of  time,  it  is  necessary  to  divide  by  360 

10 


ARMATURE  REACTION 


n 


times  the  frequency.  Another  difference  should  also 
be  pointed  out  here,  which  is  that  the  voltage  is  taken 
as  residing  in  the  active  conductors  themselves,  and  not 
at  the  hypothetical  centre  of  a  coil  formed  by  two  sets 
of  active  conductors  and  their  end  connections. 

The   most   important   thing  that   goes    round   the 
alternator  is  the  stator  flux,  namely,  that  flux  which 

, Flux 

Current- 

Stefor  Volte 


leakage  Flux 
FIG.  5. 

actually  cuts  the  stator  conductors  and  enters  the  iron 
at  the  back  of  the  stator  slots.  It  is  this  flux  which 
makes  the  stator  volts,  all  of  which  volts  are  measured 
by  a  voltmeter  at  the  terminals  of  the  machine,  except- 
ing only  those  lost  in  stator  resistance.  It  is  worth 
while  to  insist  on  this  statement,  as  there  is  so  often 
erroneously  supposed  to  be  some  larger  flux  than  this  in 
the  stator. 


12  ALTERNATING   CURRENT  DESIGN 

As  it  is  this  flux  which,  by  cutting  the  stator  con- 
ductors, makes  the  stator  volts,  these  latter  are  in  phase 
with  the  former  and  proportional  to  it.  It  follows  that 
the  stator  flux  and  terminal  voltage  can  be  represented 
by  different  lengths  of  the  same  vector,  measured  off 
each  to  its  appropriate  scale. 

The  maximum  stator  current  will  be  at  an  angle  <£ 
Currenr 


FIG.  6. 

to  the  terminal  voltage,  when  cos  </>  is  the  power  factor 
of  the  outside  circuit. 

The  next  flux  to  consider  is  the  stator  leakage  flux, 
i.e.  that  flux  which  surrounds  the  stator  conductors 
simply  from  their  own  magnetizing  force.  That  this 
flux  is  at  right  angles  to  the  position  of  the  maximum 
current  is  shown  by  the  sketch  (Fig.  6). 

The  stator  leakage  flux  runs  along  the  roofs  of  the 
stator  teeth  and  crosses  the  air  space  to  the  magnets ; 


ARMATURE  REACTION  13 

at  least,  this  is  the  final  result.  If  the  fluxes  could  be 
built  up  separately,  the  leakage  flux  would  first  of  all 
travel  along  the  roofs  of  the  stator  teeth  and  enter  the 
stator,  and  return  by  the  iron  at  the  back  of  the  stator ; 
then  the  magnet  flux  would  cross  the  air  space,  and 
part  of  it,  combining  with  the  leakage  flux,  would  form 
the  true  stator  flux  at  the  back  of  the  stator  conductors, 
and  part  of  it  would  return  to  the  magnet  circuit  vid 
the  roofs  of  the  slots,  combining  with  the  other  part  of 
the  leakage  flux. 


FIG.  7. 

There  is  also  that  flux  which  exists  in  the  magnet 
circuit  but  does  not  cross  the  air  space,  leaking  from 
pole  to  pole  of  the  magnets  ;  this  is  the  magnet  leakage 
flux,  which  is  generally  somewhat  mechanically  dealt 
with  by  means  of  a  leakage  coefficient. 

So  it  comes  about  that  the  magnet  circuit  proper 
has  to  provide  three  sets  of  lines  of  force,  one  which 
never  crosses  the  air  space  but  leaks  from  pole  to  pole, 
another  which  crosses  the  air  space  and  leaks  over  the 


1 4  ALTERNATING   CURRENT  DESIGN 

roof  of  the  stator  slots,  and  a  third  which,  cutting  the 
stator  conductors,  enters  the  stator  iron  and  constitutes 
the  working  stator  flux.  This  last  is  the  only  flux 
which  cuts  conductors  and  therefore  which  produces  volts. 
If  a  search  coil  winding  were  supported  just  clear  of  the 
pole  tips,  this  would  measure  a  voltage  proportional 
to  the  air  space  flux,  but  as  such  a  winding  does  not 
usually  exist,  it  is  a  mistake  to  translate  these  other 
fluxes  into  volts  at  all,  it  being  much  simpler  to  treat 
them  as  fluxes. 

These  various  fluxes  are  not,  however,  all  in  phase, 
i.e.  do  not  have  their  maximum  values  simultaneously, 
and  so  cannot  be  added  arithmetically.  The  vector 
diagram  shows  their  relative  magnitude  and  phase. 
The  air  space  flux  is  the  resultant  of  the  stator  flux  and 
the  stator  leakage  flux.  The  total  rotor  flux  is  obtained 
from  the  air  space  flux  by  multiplying  this  latter  by  a 
waste  field  coefficient,  although,  strictly  speaking,  the 
magnet  waste  field  or  leakage  flux  is  proportional  to  the 
excitation  and  inversely  proportional  to  the  reluctance  of 
the  leakage  paths,  and  is  not  connected  with  the  main 
flux  in  any  very  simple  way. 

These  three  fluxes  having  been  determined,  and  the 
areas  of  the  magnetic  paths  calculated,  a  synthesis  can 
be  made  in  the  usual  way,  but  using  the  three  different 
fluxes  for  the  stator,  the  air  space,  and  the  magnet 
circuit  respectively.  This  synthesis  will  give  the  ampere 
turns  required  to  get  the  full  load  fluxes  through  the 
magnetic  circuit,  and  it  now  remains  to  add  to  these  an 
extra  amount  to  overcome  the  demagnetizing  effect  of  the 


ARMATURE  REACTION  15 

stator  currents.  To  do  this  draw  a  vector,  representing 
in  length,  to  some  convenient  scale,  the  ampere  turns 
from  the  combined  synthesis,  and  make  its  direction 
parallel  to  the  vector  representing  the  air  space  flux  in 
the  flux  diagram  (Fig.  5).  The  demagnetizing  stator 
ampere  turns  are  at  right  angles  to  the  stator  current  and 
parallel  to  the  stator  leakage  flux  (see  Fig.  6)  ;  drawing 
these  to  the  same  scale  of  ampere  turns  from  the  same 


Sfator 

demagnetizing 
AT.  5 

FIG.  8. 

point  as  the  ampere  turns  from  the  synthesis,  the 
resultant  of  the  two  gives,  to  the  same  scale,  the  total 
ampere  turns  required  on  the  rotor  for  full  load  at  the 
particular  power  factor  chosen. 

Let  us  now  consider  the  actual  numerical  values  of 
the  various  quantities  we  have  been  using.  Firstly  the 
stator  flux;  this  is  obtained  from  the  total  volts  by 
multiplying  these  latter  by  v/2  and  108  and  dividing  by 
277^  and  the  turns  in  series.  The  total  volts  are 


1 6  ALTERNATING   CURRENT  DESIGN 

simply  the  terminal  volts  added  to  those  lost  in  the  stator 
resistance  ;  strictly  speaking,  vector  addition  should  be 
employed  for  power  factors  less  than  unity,  as  the 
lost  volts  are  in  phase  with  the  current,  and  this  in 
reality  throws  the  stator  flux  slightly  out  of  phase 
with  the  terminal  volts.  In  practice,  however,  the  volts 
lost  in  resistance  are  so  small  a  fraction  of  the  terminal 
volts  that  this  refinement  is  not  worth  putting  into  force, 
and  the  total  volts  are  taken  as  the  arithmetical  sum  of 
the  terminal  and  lost  volts. 

The  stator  leakage  flux  may  be  arrived  at  in  various 
ways,  the  first  of  which  consists  in  consulting  the 
results  of  the  many  excellent  published  experiments 
which  give  the  leakage  lines  of  force  per  inch  length  of 
slot  per  ampere  in  the  slot  for  various  different  shapes 
of  slots.  The  figure  for  this  leakage  flux  varies  from 
about  50  in  parallel  to  100  in  roofed  slots ;  this  has  of 
course  to  be  multiplied  by  the  length  of  the  slot  and  by 
the  current  flowing  in  the  conductors  in  the  slot.  Some 
allowance  should  also  be  made  for  leakage  lines  round 
the  end  connections,  this  again  being  affected  by 
whether  all  the  end  connections  from  one  pole  are 
collected  together  so  that  each  is  cut  by  the  lines  made 
by  all  the  others,  or  whether  the  end  connections  are 
more  separated,  being  cut  only  by  their  own  or 
immediate  neighbours'  lines. 

The  rotor  waste  field  coefficient,  though  depending  on 
many  other  things  than  those  mentioned  in  the  following 
formula,  may,  in  the  absence  of  more  definite 
experimental  data,  be  approximately  represented  by 


ARMATURE  REACTION  17 


/   0*2  x  poles 
1  +  ^y        diameter     ;  the  magnet  flux  bemS  the  air 

space   flux  x  w.f.c.,    and   the   diameter   being   that  of 
the  air  space  in  inches. 

The  next  quantity  to  evaluate  is  the  demagnetizing 
effect  of  the  stator  current.      In  a  single-phase  stator 
winding  the  maximum  value  of  the  ampere  turns  per 
pole  is  \/2  X  E.M.S.  current  x  turns  per  pole  ;  that  the 
magnetic  effect  of  this  winding  may  be  split  up  into 
two  equal  parts  revolving  round  the  stator  in  opposite 
directions   with   the   speed   of    the    field    magnets    is 
susceptible  to  mathematical  proof  as  well  as  to  experi- 
mental verification.      That  part  which  revolves   in    a 
direction   opposite    to    that    of  the   magnets   has   no 
resulting   demagnetizing   effect,    producing    merely    a 
surge   in   the   flux   of    twice    the    frequency    of    the 
alternator ;  that  half  which  revolves  at  the  same  speed 
as  the  magnets  and  in  the  same  direction  is  consequently 
stationary  with  regard  to  the  magnet  poles  and  exercises 
a  demagnetizing  effect  on  them,  in  amount  equal  to 
ha]f  the  maximum  ampere  turns,  and  in  phase,  at  right 
angles  to  the  stator  current.     In  multiphase  windings 
the  total  turns  per  pole  of  all  phases  are  of  course  taken, 

V/2 

and  the  demagnetizing  ampere  turns  are  --=-  x  E.M.S. 

Zi 

current  per  phase  x  total  turns  per  pole  on  all  phases. 

We  have  now  all  the  data,  not  only  to  determine 
the  requisite  strength  for  the  magnet  winding  of  an 
alternator,  but  also  to  predict  its  voltage  regulation  at 
all  power  factors  and  loads. 

o 


i8  ALTERNATING   CURRENT  DESIGN 

The  "  Inherent  Regulation "  of  an  alternating 
current  generator  is  defined  by  the  British  Standards 
Committee  as  the  rise  in  terminal  voltage  on  full  load 
being  thrown  off  at  the  specified  power  factor,  both  the 
speed  and  the  excitation  being  kept  unaltered.  This 
rise  can  be  kept  down  by  two  methods,  firstly  by  making 
the  increase  of  magnetizing  force  from  open  circuit 
to  full  load  small,  which  may  be  done  either  by  keeping 
the  stator  leakage  flux,  or  the  stator  ampere  turns 
per  pole,  or  both,  low  ;  and  secondly,  whilst  allowing 
the  full  load  magnetization  to  be  largely  in  excess  of 
that  required  for  open  circuit,  the  inductions  in  some 
or  all  of  the  magnetic  circuit  may  be  normally  so  high 
that  the  large  number  of  ampere  turns  set  free  on 
throwing  off  the  load  may  be  unable  to  produce  more 
than  a  slightly  increased  flux,  and  therefore  volts,  on 
open  circuit. 

In  most  cases  the  first  method  mentioned  will  give 
rise  to  an  alternator  which  requires  less  attention  in 
actual  running,  but  the  latter  method  will,  in  general, 
make  the  cheaper  design  to  build,  and  would  be  oftener 
employed  by  the  designer  when  working  to  a  given 
inherent  regulation  specified  in  this  way,  were  it  not 
for  a  certain  element  of  risk  which  is  always  present  in 
using  these  high  inductions — that  a  small  error  may  be 
made  in  estimating,  say,  the  stator  leakage  flux  or  the 
rotor  waste  field  coefficient,  thus  making  it  difficult  or 
impossible  to  obtain  the  required  voltage,  especially  at 
low  power  factors. 

Another   method    of   defining  the  regulation  is  by 


ARMATURE  REACTION  19 

the  drop  in  terminal  voltage  from  open  circuit  to  full 
load.  This  is  framed  to  prevent  the  obtaining  of  good 
regulation  by  high  inductions  as  above,  but  is,  however, 
unsatisfactory  from  other  reasons,  one  of  which  is  that 
"  full  load  "  can  never  be  obtained  with  the  open  circuit 
excitation ;  in  many  alternators  full  load  current  even 
would  not  be  reached  if  the  alternator  were  short- 
circuited  with  the  open  circuit  excitation.  Obviously, 
the  regulation  should  not  be  specified  or  tested  under 
conditions  so  far  removed  as  this  from  actual  practice. 
All  interests  would  be  safeguarded  by  specifying  the  rise 
in  terminal  voltage  on  throwing  off  full  load,  together 
with  the  ratio  of  full  load  to  open  circuit  excitation. 


CHAPTER   III 

RELATION    OF   DIMENSIONS  TO    OUTPUT 

ONE  of  the  most  obvious  limitations  which  imposes 
itself  on  all  running  machinery,  whether  for  direct  or 
alternating  current,  is  the  density  of  current  round  the 
air  space,  the  number  of  amperes  in  unit  arc  of 
circumference. 

In  this  way  can  be  expressed,  not  only  the  electro- 
magnetic effect  of  so  much  concentrated  current,  but 
also  the  physical  possibility  of  packing  the  conductors 
carrying  such  current  into  the  space  at  our  disposal. 

Taking  the  latter  limitation  first,  it  is  readily  seen 
that  1000  amperes  per  inch  of  circumference,  combined 
with,  say,  1000  amperes  per  square  inch  of  conductor, 
would  require  a  depth  of  winding  not  possibly  less 
than  an  inch,  and  with  teeth  and  slots  of  equal  width 
at  50  per  cent,  space  factor  in  the  latter,  4  inches 
deep. 

Not  less  is  it  a  limit  to  armature  reaction,  for  the 
effect  of  the  armature  current  on  the  magnet  system  is 
obviously  proportional  to  the  concentration  of  the 
former. 

Now,  the  term  "  amperes  per  unit  arc  of  circum- 
ference," although  expressing  just  what  is  wanted,  is 

20 


RELATION  OF  DIMENSIONS   TO   OUTPUT  21 

cumbrous,  partly  because  it  is  the  diameter  which  is 
usually  measured,  not  the  circumference,  and  also 
because  there  seems  to  be  a  disinclination  to  think  of 
current  as  disassociated  from  the  conductor  it  is 
flowing  in ;  so  that  the  expression  has  gone  through 
the  forms  "  ampere  conductors  per  unit  of  circum- 
ference," "  ampere  conductors  per  unit  of  diameter/'  to 
"ampere  turns  per  inch  diameter,"  the  last  change 
from  ampere  conductors  to  ampere  turns  being 
particularly  indefensible,  as  it  is  not  in  the  effect  of  a 
closed  ampere  turn  that  the  phenomenon  is  being 
studied  at  all,  turns  being  merely  equivalent  to 
"  conductors  divided  by  two." 

Not  only  do  the  ampere  turns  per  inch  diameter 
form  a  limit  to  every  class  of  revolving  electrical 
machinery,  but  in  all  the  value  of  this  constant  is  nearly 
alike,  varying  from  about  800  to  1200,  according  to 
size,  etc. 

The  magnetic  induction  in  the  air  space  is  another 
quantity  which  it  is  not  advisable  to  vary  far  from 
certain  prescribed  limits,  which  are,  on  the  one  hand,  the 
proper  use  of  material  to  the  best  advantage,  and,  on  the 
other,  the  maximum  allowable  induction  in  the  teeth 
and  the  limits  to  magnetizing  force  on  the  rotor.  The 
proper  compromise  between  these  two  may  lie  some- 
where about  a  maximum  induction  of  8000  lines  per 
square  centimetre  of  air  space. 

Taking  this  figure  in  conjunction  with  one  for  the 
ampere  turns  per  inch  diameter  of  800,  we  get  that 
the  square  of  the  diameter  multiplied  by  the  axial 


22  ALTERNATING   CURRENT  DESIGN 

length  of  the  alternator  is  equal  to  the  output  at  one 
revolution  per  minute  divided  by  0'031.     For  let 

E  =  R.M.S.  volts 

C  =  R.M.S.  amperes 

N  =  lines  of  force  per  pole 

T  .=  total  turns  on  stator 

R  =  revolutions  per  minute 

D  =  air  space  diameter  in  inches 

L  =  axial  length  in  inches 

P  =  number  of  poles. 

Assuming  a  sine  wave  distribution  of  lines  over  the 
air  space 

the  maximum  induction  =  ^, 
the  averae  =  -~  X 


-~       ~T)/  x  6'45 
from  which 

PN  =  DZ  x  2  x  6-45  x  8000 

CT 

The  ampere  turns  per  inch  diameter  =  -^-  =800, 

or  T  =       x  800 


Now  N  = 

and  ^  — 


27T~  T 

PR 

120 


,         .,  ^^        E        \/2  x  120  x  108 

irom  these  two          PN  =         x 


ZTT 

Putting  in  the  value  of  T  from  above,  and  equating  to 
the  first  value  of  PN,  we  get  that 

P 

-  =  D2/  x  0-031. 


RELATION  OF  DIMENSIONS   TO   OUTPUT  23 

The  similar  constant  for  direct- current  generators  with 
the  same  ampere  turns  per  inch  diameter,  reactance 
volts  of  5,  and  volts  per  commutator  bar  of  10,  is  0'034. 

Besides  these  two  more  or  less  theoretical  limitations 
there  are,  in  alternating- current  generators,  certain 
limitations  arising  out  of  the  least  convenient  pole  pitch 
which  can  be  used  for  internally  revolving  magnets. 
One  would  not  willingly  make  the  core  of  the  magnet 
pole  less  than  3  inches  circumferentially  ;  putting  \\ 
inches  of  winding  on  each  side  of  this  and  allowing  1 
inch  for  insulations  and  clearance,  makes  a  pole  pitch  of 
7  inches.  This  can  be  expressed  by  saying  that  the 
diameter  must  not  be  less  than  the  number  of  poles 
multiplied  by  2*2. 

The  peripheral  speed  of  the  magnets  imposes  a  limit 
in  the  other  direction.  If  we  limit  this  to,  say,  8000 
feet  per  minute,  by  simple  arithmetic  the  diameter 
cannot  be  more  than  the  number  of  poles  multiplied  by 
250  and  divided  by  the  frequency  ;  which  gives,  at  <^25, 
10  times  the  number  of  poles,  and  at  ^100,  2*5  times. 
Comparing  this  last  figure  with  the  statement  in  the 
preceding  paragraph  that  the  diameter  should  not  be 
less  than  2'2  times  the  poles,  it  is  seen,  what  is  indeed 
found  to  be  the  case,  that  at  frequencies  above  100 
either  the  poles  would  be  crowded  or  the  peripheral 
speed  high. 


CHAPTER  IV 

EXAMPLE    OF   THE   DESIGN    OF   AN   ALTERNATOR 

To  illustrate  the  foregoing,  we  will  now  proceed  to  the 
design  of  an  alternating  current  generator  to  fulfil  the 
following  specification  :  Output,  250  kilowatts  at  any 
power  factor  from  unity  to  0'8  ;  1000  volts  3-phase 
50  ^,  375  r.p.m.  ;  overloads,  25  per  cent,  for  2  hours, 
50  per  cent,  for  5  minutes.  Temperature  rise  not  to 
exceed  40°  Centigrade  after  6  hours  at  250  KW.  at 
0'8  power  factor.  Inherent  regulation,  not  more  than 
6  per  cent,  rise  at  p.f.  1,  and  20  per  cent,  rise  at  p.f. 
0*8  when  full  load  is  thrown  off,  keeping  the  speed  and 
excitation  unaltered. 

Star  wound,  the  volts  per  phase  will  be  577,  the 
current  per  phase  p.f.  1  will  be  144  amperes,  and  p.f.  0'8 
180  amperes  ;  25  per  cent,  overload  at  the  lower  p.f.  is 
225,  and  50  per  cent.  270  amperes. 

Number  of  poles  is  16  for  50  ^at  375  r.p.m. 

First,  as  to  diameter,  the  various  guides  given  in 
the  last  chapter  are  :  Firstly,  the  D2Z  formula  for  a 
length  of  10  inches,  which  would  give  for  312'5  K.V.A., 
a  diameter  of  52  inches  ;  secondly,  the  least  diameter, 
from  reasons  of  crowding  magnets,  would  be  48  inches  ; 
and,  thirdly,  the  greatest  diameter,  from  questions  of 

24 


EXAMPLE   OF  THE  DESIGN  OF  AN  ALTERNATOR     25 

peripheral  speed,  would  be  82  inches.  Obviously,  it  is 
not  good  practice  to  approach  too  near  to  either  of  the 
last  two  limits,  and  so,  in  the  absence  of  any  guide 
afforded  by  the  nearest  pattern  in  stock,  we  will  choose 
a  diameter  of  60  inches  bore  of  stator  plates. 

The  total  turns  to  give  800  ampere  turns  per  inch 
diameter  at  60  inches  would  be  266,  or  89  per  phase. 
For  a  two-plane  winding  on  the  stator  there  cannot 
conveniently  be  less  than  two  conductors  per  slot,  also 
there  must  be  a  whole  number  of  slots  per  pole  per 
phase.  Making  this  five  gives  80  turns  per  phase,  and 
240  as  the  total  number  of  slots. 

Stator  winding,  180  amperes  at,  say,  1800  amperes 
per  square  inch,  gives  O'l  square  inch  for  the  area  of 
the  copper.  Try  0'4"  x  0'25"  insulated  with  0'05"  of 
micanite  all  round.  The  covered  conductor  will  be 
0'5"  X  0'35".  A  slot  0'4"  wide  will  allow  of  a  slot  lining  of 
leatheroid  to  protect  the  micanite  from  the  edges  of  the 
plates.  Two  0*5"  conductors  and  a  strip  of  hard  wood 
will  go  in  to  a  depth  of  1*25".  So  that  we  have  240 
slots  1*25"  x  0*4".  The  next  step  is  to  estimate  the 
resistance  of  the  stator  circuits  in  order  to  get  the  total 
volts  and  thus  the  stator  flux.  This  involves  knowing 
the  length  of  the  stator  plates  parallel  to  the  shaft; 
assume  this  to  be  10".  The  end  connections  may  like- 
wise be  assumed  to  form  the  sides  of  an  equilateral 
triangle  with  the  pole  pitch  as  base.  The  pitch  of  16 
poles  at  60"  diameter  is  12",  so  that  the  length  of  each 
turn  will  be  about  2  x  10  +  4  X  12  =  68".  The 
resistance  of  one  phrase  of  80  such  turns,  allowing  a 


26  ALTERNATING   CURRENT  DESIGN 

temperature  of  60°  C.  would  be  0*042  ohm  but  for  the 
fact  that  20"  of  the  conductor  is  embedded  in  iron  and 
cut  by  its  own  leakage  flux,  which  produces  a  local 
current  which  circulates  along  the  top  half  of  the 
embedded  conductor  and  back  in  the  lower  half ;  this 
eddy  current  combines  with  the  main  current,  adding 
in  the  top  half  and  subtracting  in  the  lower  half  of  the 
conductor,  the  net  result  being  that  the  current  appears 
to  be  crowded  up  into  the  top  edge  of  the  conductor,  thus 
causing  a  larger  ohmic  drop  than  if  it  distributed  evenly 
throughout  the  section.  Mr.  M.  B.  Field  has  published 
a  curve  in  which  the  increase  of  ohmic  resistance  of 
the  embedded  conductor  is  plotted  against  a  quantity 
"  mb  "  (see  the  Journal  of  the  Institution  of  Electrical 
Engineers,  vol.  37,  p.  101).  mb  =  area  of  the  conductor  in 

/  "0  13  X  ^ 

sq.   in.  x      /  width  of  conductor"  x  width  of  slot  " 

In  the  present  case  mb  would  equal  0*8  ;  referring  to 
the  curve  we  find  that  the  resistance  of  the  bottom  con- 
ductor will  be  increased  4  per  cent. ,  and  that  of  the  top 
conductor  30  per  cent.  This,  of  course,  only  applies  to 
two  lengths  of  10"  each  out  of  a  total  of  68",  so  the 
whole  resistance  will  be  increased  5  per  cent. 

The  volts  lost  in  resistance  at  the  normal  current  of 
180  amperes  will  therefore  be  8  per  phase,  making  a 
total  of  585,  which  corresponds  to  a  stator  flux  of 

\/2  X  585  X  108 
27T  X  50  x  80     =  3'3  X  10  lmes  Per  P°le' 

The  area  required  for  the  teeth  to  carry  this  flux  at 
a  maximum  induction  of  17,000  lines  per  cm2,  is  30  sq.  in. 


EXAMPLE   OF   THE  DESIGN  OF  AN  ALTERNATOR     27 

If  the  width  of  the  pole  face  is  such  that  the  winding  of 
one  phase  occupies  the  gap  between  the  poles  at  one 


0-24*|06 


FIG,  9. 


instant,  then  there  are  1 1  teeth  to  carry  the  lines  from 


28  ALTERNATING   CURRENT  DESIGN 

each  pole.  The  pitch  of  240  teeth  at  60"  diameter  is 
079",  the  slot  is  0'4"  of  this,  leaving  0'39"  for  the 
tooth ;  the  length  of  iron  required  is  therefore  the  30 
sq.  in.  divided  by  11  times  0*39"  =7". 

Using  plates  0'014"  thick  for  the  stator,  and  in- 
sulating them  with  O'OOl"  varnish  each  side,  the 
insulated  plates  will  measure  8" ;  putting  three  |" 
ventilation  spaces  into  this  makes  9*5"  overall  length 
of  core  plates. 

The  area  required  for  an  induction  of  say  8000  at 
the  back  of  the  slots,  is  32  sq.  in.,  which  divided  by 
the  net  length  of  iron  gives  4 "6"  depth  radially.  The 
outside  diameter  of  the  stator  plates  would  then  be 
60  +  2  x  T25  4- 2x4-6  =  717";  make  this  72",  which 
gives  an  induction  of  7700  lines  per  cm2. 

The  slot  leakage  flux,  assuming  50  lines  per  ampere 
per  inch  length  of  slot,  at  a  current  of  180  amperes, 
amounts  to  50  x  180  x  A/2  x  9'5  =  0'24  x  106. 

The  angle  whose  cosine  is  0'8  is  37  degs.,  so  that 
the  stator  flux  and  the  stator  leakage  flux  are  at  an 
angle  of  90  4-  37,  or  127  degrees.  Drawing  the  two 
vectors  3*3  x  106  and  0'24  x  106  at  this  angle,  the 
resultant  is  found  to  be  3*45  X  106,  which  is  the  flux  in 
the  air  space. 

The  waste  fieM  coefficient,  indicated  by  the  formula 
in  Chapter  II  would  be  1*22,  say  1*25  for  safety.  The 
rotor  flux  is  then  4*3  X  106.  To  accommodate  this  in 
steel  at  B  =  17,000  needs  39  sq.  in.  5"  X  9"  with  semi- 
circular ends  gives  39*6  sq.  in.  and  16,700  lines  per  cm2. 
Before  settling  on  these  dimensions  for  the  pole,  it  is 


EXAMPLE   OF  THE  DESIGN  OF  AN  ALTERNATOR     29 

wise  to  see  if  they  allow  sufficient  room  for  the  magnet 
winding.  Assuming  a  6"  length  for  the  pole,  and  J"  a 
side  for  the  clearance  between  stator  and  rotor,  the  out- 
side diameter  of  the  yoke  is  47|",  making  the  pole 
pitch  there  9*3".  Allowing  J"  clearance  between  coil 
and  pole  and  J"  between  coils,  the  minimum  depth  of 
the  coil  is  1*7",  and  assuming  a  depth  of  l"  for  the  pole 


FIG.  10. 

tip  the  maximum  depth  of  the  coil  is  2'  6"  and  the 
height  4*5",  which  gives  an  area  for  winding  of  9*7  sq.  in., 
which  should  be  sufficient  (Fig.  10). 

The  thickness  of  the  pole  tip  next  deserves 
attention.  The  pole  arc  has  already  been  settled  at  two- 
thirds  of  the  pole  pitch,  or  7*8".  The  flux  from  this  to  the 
air  space  is,  we  have  seen,  3*45  X  106  lines,  whilst  the 
flux  in  the  magnet  core  is  4*3  X  106.  Two  assumptions 
are  now  made,  each  on  the  safe  side  ;  firstly,  that  the 


30  ALTERNATING   CURRENT  DESIGN 

flux  to  the  air  space  is  uniformly  distributed  over  the  pole 
face,  and  secondly  that  all  the  rotor  waste  field  passes 
through  the  pole  tips,  so  that  the  flux  which  does  not 

do  so  is  A.  of  3-45  x  106  =  2 '2  X  106.     The  rest,  or 

7*8 

4*3  —  2*2  =  2*1  X  106  lines,  must  pass  into  the  pole 
tips  from  the  magnet  core  ;  at  18,000  B  this  requires 
18  sq.  in.,  or  9  sq.  in.  each  side  ;  the  length  of  the  pole  tip 
is  9j",  so  that  l"  thickness  at  the  centre  will  be 
satisfactory. 

The  yoke  ring,  if  of  cast  iron  may  be  worked  at 
about  8000  lines  per  cm2.,  and  would  then  require  an 
area  of  42  sq.  in.  or  say  12"  x  3j".  If  this  is  done,  some 
provision  must  be  made  for  the  lines,  which  are  at  an 
induction  of  17,000  in  the  steel,  to  enter  the  cast  iron 
at  not  more  than  half  this.  This  may  be  done  by 
providing  the  steel  poles  with  enlarged  bases  where 
they  abut  against  the  cast  iron  ;  these  could  be  9"  x  9" 
X  l"  thick  in  this  case.  Or  again,  the  steel  poles  could 
be  recessed  into  the  cast  iron.  In  the  former  case  the 
pole  tip  would  have  to  be  separate,  and  might  very  well 
be  laminated  in  the  same  plane  as  the  stator  plates. 

This  finishes  the  outward  design  with  the  exception 
of  the  magnet  winding  ;  for  this  a  synthesis  of  the  mag- 
netization is  required.  This  differs  from  the  ordinary 
only  in  the  use  of  the  three  fluxes  already  obtained  for  the 
stator,  air  space  and  rotor  circuits  respectively.  The  area 
of  the  teeth  is  taken  as  that  at  one-fifth  of  their  length 
from  the  small  end,  and  the  area  of  the  air  is  one-fifth  of 
the  way  between  the  pole  face  and  the  tops  of  the  teeth, 


EXAMPLE   OF  THE  DESIGN  OF  AN  ALTERNATOR     31 


i.e.  four  times  the  pole  face  area  is  added  to  the  minimum 
tooth  area  and  the  sum  divided  by  5.  This  process  has 
no  theoretical  basis,  and  its  only  justification  is  that  it 
usually  checks  very  closely  with  the  observed  facts. 

SYNTHESIS  OF  MAGNETIZATION  AT  FULL  LOAD  P.F.  0'8. 


Magnetic  circuit. 

HxZ 

Length 
cms. 

Area 

cms2. 

Flux 
X  106. 

lines  per 
cm". 

H 

per  cm. 

C.G.S. 
units  per 
2  poles. 

Stator  core  X  2 

33-5 

430 

3-3 

7,700 

2 

67 

Teeth  1          

6-85 

197 

3-3 

16,800 

36 

228 

Air  space  \   

1-27 

420 

3-45 

8,210 

8210 

10,430 

Magnet  cores 

31-0 

256 

4-3 

16,800 

61 

1,890 

Yoke  X  2      

20-0 

540 

4-3 

8,000 

26 

520 

Magnetizing  force  =  5,250  A.T.'s  per  pole  =  13,135 


To  these  5250  ampere  turns  per  pole  must  be 
added,  at  the  proper  angle,  the  ampere  turns  to  com- 
pensate for  armature  reaction;  these,  from  Chapter II. 


180  x  *—  =  1910  A.T.'s.    Putting  these  on  to 

the  vector  diagram,  Fig.  9,  measuring  one  off  on  the  direc- 
tion of  air  space  flux  and  the  other  on  the  direction  of 
stator  leakage  flux,  we  arrive  at  the  result  that  6650 
ampere  turns  are  required  per  pole  on  the  rotor  when 
the  alternator  is  doing  1000  volts  180  amperes  at  0'8 
power  factor. 

But  the  alternator  has  also  to  give  for  five  minutes  a 
50  per  cent,  overload ;  the  rotor  winding  will  therefore 
have  to  magnetize  for  this. 

The  increase  in  the  stator  flux  brought  about  by 
the  increased  resistance  drop  may  be  neglected,  but  the 
stator  leakage  flux  is  increased  50  per  cent,  to  0'36  X  106 


32  ALTERNATING   CURRENT  DESIGN 

lines  ;  this  increases  the  air  space  flux  to  3*53  X  106  and 
the  rotor  flux  to  4*41.  If  the  combined  synthesis  is 
worked  out  for  these  new  fluxes,  the  ampere  turns 
are  found  to  have  increased  from  5250  to  5550  per 
pole.  The  demagnetizing  A.T.'s  are  increased  50 
per  cent,  to  2860,  which  on  the  vector  diagram  results 
in  7750  A.T.'s  total  for  50  per  cent,  overload  at  a  p.f. 
of  0'8. 

The  rotor  winding  should  give,  therefore,  at  least 
8000  A.T.'s  when  warm,  for  a  few  minutes,  and  6650 
A.T.'s  under  the  temperature  rise  specification. 

The  mean  depth  of  the  magnet  coil  is  2*15".  This 
is  wound  round  a  core  9"  x  5"  with  semicircular  ends, 
with  J"  clearance  from  the  steel ;  this  makes  the  length 
of  the  mean  turn  2  x  4  +  TT  x  7*65  =  32". 

Now  the  ampere  turns  are  dependent  on  the  area  of 
the  wire  only  and  not  on  the  number  of  turns,  so  that 
if  we  excite  from  a  100- volt  circuit  the  resistance  of 
one  turn  per  pole  must  be  such  as  to  allow  800 
amperes  to  flow;  i.e.  16  x  32  =  512  inches  must  have 
a  resistance  warm  of  0*0125  ohm,  so  that  the  area 
required  is  0'0315  sq.  in.  In  round  wire  the  diameter 
would  be  0*2",  or  double  cotton-covered  0'216".  This  at 
1000  amperes  per  sq.  in.  will  carry  31*5  amperes,  which 
current  gives  the  required  full  load  excitation  of  6650 
A.T.'s  with  210  turns.  The  space  required  for  this 
would  be  210  x  0'216*  =  9'8in2.  The  space  available 
is  9'7  in2.,  into  which  200  turns  of  such  wire  will  go 
nicely. 

The  resistance  of  16  poles  in  series  will  be   2*17 


EXAMPLE   OF    THE  DESIGN  OF  AN  ALTERNATOR     33 


ohms  cold,  or  2*5  ohms  at  60°  C.  The  loss  in  the 
magnets  at  full  load  will  be  2'5  x  33'252  =  275  KW., 
which  is  0'88  per  cent,  of  the  K.V.A.  output. 

Before  the  entire  behaviour  of  the  alternator  can  be 
predicted  an  open  circuit  magnetization  curve  must 
be  worked  out.  This  is  done  on  the  same  lines  as  the 
previous  synthesis,  but  with  no  stator  leakage  flux,  the 
same  waste  field  coefficient  being  used  for  the  magnet 
circuit.  Four  points,  if  well  chosen,  will  be  sufficient 
to  draw  this  curve  through.  Take  2,  3,  3 '5,  and  4 
million  lines  in  the  stator,  corresponding  to  615,  920, 
1080,  and  1230  line  volts  at  375  r.p.m.  respectively. 

The  areas  and  lengths  of  the  magnetic  circuits  are, 
of  course,  the  same  as  for  the  last  synthesis,  and  are 
not  here  repeated. 

OPEN  CIRCUIT  SYNTHESIS. 


Line  volts 

615 

920 

1080 

1230 

Flux  X  108 

2 

3 

3-5 

4 

B  and  H,  Stator 
Teeth 
Air 
Magnets 
Yoke 

4,650  -  1 
10,100  -  3 
4,760 
9,750  -  3-5 
4,630  -  13 

7,000  -  1-5 
15,200  -  13 
7,140 
14,600  -  17 
6,950  -  20 

8,150  -  2 
17,700  -  82 
8,330 
17,000  -  68 
8,100  -  27 

9,300  -  2-5 
20,200  -  300 
9,520 
19,500  -  300 
9,250  -  36 

H  X  l,       Stator 
Teeth 
Air 
Magnets 
Yoke 

33 
19 
6,050 
108 
260 

50 
82 
9,070 
527 
400 

67 
520 
10,580 
2,110 
540 

85 
1,900 
12,090 
9,300 
720 

C.G.S.  per  2  limbs 

6,470 

10,129 

13,817 

24,095 

A.T.'s  per  pole 

2,590 

4,050 

5,530 

9,640 

34 


ALTERNATING   CURRENT  DESIGN 


Fig.  11  shows  the  result,  line  volts  at  375  revolutions 
per  minute  being  plotted  against  ampere  turns  per  pole. 

This  curve  shows  that  the  full  load  0'8  power  factor 
excitation  of  6650  A.T.'s  gives  on  open  circuit  1150 
volts,  or  15  per  cent,  rise  on  throwing  off  this  load, 
which  is  5  per  cent,  within  the  guarantee. 

OPEN  CIRCUIT  MAGNETIZATION  CURVE. 


1500 
1400 
1300 
1  200 

1  100 
1000 

!9~ 

1C  800 

CO 

rt    700 
>    600 

.£  5oo 


400 


300 


T 


3000         4000         5000         6000         7000 
Ampere  Turns  per  pole  on  Rotor. 

FIG.  11. 


8000 


9000 


Allowing  a  3  per  cent,  rise  in  speed  on  open  circuit, 
the  excitation  per  1000  volts  is  seen  to  be  4400  A.T.'s  ;  to 
get  this  from  the  100  volt  supply  would  need  a  resist- 
ance of  2*36  ohms  in  series  with  the  magnets,  graduated 
to  carry  a  current  of  from  22  amperes  when  all  in  circuit 
to  40  amperes  on  the  last  point. 

We  have  already  enough  data  to  draw  the  curve, 


EXAMPLE   OF   THE  DESIGN  OF  AN  ALTERNATOR     35 


which  is  very  nearly  a  straight  line,  between  the 
current  per  phase  and  the  ampere  turns  required  on 
the  magnets  to  maintain  1000  volts  at  0*8  power  factor 
at  375  r.p.m.  The  points  are  these :  No  current,  4650 
A.T.'s;  180  amperes,  6650  A.T.'s ;  270  amperes,  7750 
A.T.'s  (Fig.  12). 

LOAD  CURVES. 


300 


tn  ioo 


3000         4000         5000         6000         7000         8000 
Ampere  Turns  per  pole  on  Rotor. 

FIG.  12. 


9000         10,000 


At  unity  power  factor,  full  load  current  is  144 
amperes,  the  stator  flux  3*29,  and  the  stator  leakage 
0'19  x  106  lines;  these  two  at  right  angles  result  in 
an  air  space  flux  of  3 '3  X  106.  As  these  are  so  nearly 
alike,  it  will  be  quite  accurate  to  lookup  3*3  x  106  lines, 
which  are  equivalent  to  1015  line  volts,  on  the  open 
circuit  magnetization  curve,  where  it  corresponds  to 


36  ALTERNATING   CURRENT  DESIGN 

4800  A.T.'s.  The  demagnetizing  ampere  turns  for  144 
amperes  are  1540;  these  two,  on  the  vector  diagram, 
have  a  resultant  5150  A.T.'s,  which  is  therefore  the 
magnetization  required  for  full  load  power  factor  unity. 

5150  A.T.'s  on  the  open  circuit  curve  correspond  to 
1050  volts,  or  a  rise  of  5  per  cent,  on  unity  p.f.,  which 
is  1  per  cent,  within  the  guarantee. 

It  is  interesting  to  see  what  would  happen  on  zero 
power  factor.  Here  the  stator  and  stator  leakage 
fluxes  would  add;  taking  the  144  amperes  the  fluxes 
are  3'29  +  0'19  =  3'48  x  106  for  the  air  space  flux. 
We  have  a  combined  synthesis  worked  out  for  3 '4 5 
X  106  lines  on  the  air  space,  which  gave  5250  A.T.'s,  so 
we  may  take  5350  A.T.'s  for  3'48.  These  again  add 
to  the  1540  demagnetizing  A.T.'s,  making  a  total  of 
6890  ampere  turns  per  1000  volts  144  amperes  at  zero 
power  factor. 

On  Fig.  12  are  plotted  these  three  curves  connecting 
amperes  per  phase  in  the  stator  with  ampere  turns  per 
pole  on  the  rotor  to  maintain  1000  terminal  volts  at 
power  factor  zero,  0'8  and  unity  respectively.  From 
these  can  be  plotted  curves  connecting  A.T.'s  per  pole 
on  the  rotor  with  the  power  factor  of  some  constant 
current  from  the  stator.  Two  of  these  have  been  drawn 
for  144  and  180  amperes,  they  serve  to  show  how  very 
fast  the  excitation  has  to  be  increased  for  the  first 
small  falling  away  from  unity  on  the  part  of  the  power 
factor ;  for  instance,  on  the  180  ampere  curve,  the 
alteration  from  unity  to  0*85  p.f.  is  greater  than  from 
0'85  to  zero. 


EXAMPLE   OF  THE  DESIGN  OF  AN  ALTERNATOR     37 

It  is  often  necessary  to  know  what  current  would 
result  if  the  alternator  were  short-circuited  at  its 
terminals  with  full  load  excitation.  The  converse  of 
this  is  easier  to  calculate,  i.e.  the  excitation  for  a  certain 
current  on  short  circuit.  As  the  short-circuit  current 
is  very  nearly  proportional  to  the  excitation,  it  is 
immaterial  what  is  the  particular  current  chosen,  so 
take  500  amperes.  The  terminal  voltage  being  zero, 
the  only  flux  in  the  stator  is  that  required  to  generate 
sufficient  volts  to  overcome  the  stator  resistance.  At 
500  amperes  this  is  22  volts  per  phase,  which  requires 
a  stator  flux  of  0*125  X  106  lines.  The  stator  leakage 
flux  will  be  0'67  x  106,  the  resultant  of  these  at  right 
angles  is  0'682  x  106,  which  corresponds  to  208  line 
volts,  which,  on  the  open  circuit  curve,  requires  850 
A.T.'s.  The  demagnetizing  A.T.'s  for  500  amperes  are 
5300  ;  the  resultant  of  these  two  on  the  vector  diagram 
is  6100.  The  full  load  0'8  p.f.  excitation  is  6650,  so 
that  the  short-circuit  current  will  be  larger  than  500 
in  that  ratio,  or  540  amperes.  This  is  exactly  three 
times  the  normal  current  of  180. 

In  calculating  the  efficiency  of  an  alternator  the 
most  difficult  of  the  losses  to  estimate  is  that  in  the 
stator  plates.  The  theoretical  value  of  the  hysteresis 
and  eddy  current  loss  is  always  largely  exceeded,  due 
partly  to  the  imperfect  insulation  between  the  plates, 
partly  to  the  fact  that  the  magnetic  lines  of  force 
are  not  always  in  the  plane  of  lamination  and  still 
more  to  the  treatment  to  which  the  plates  have  un- 
avoidably to  be  subjected  during  the  building  up  and 


38  ALTERNATING   CURRENT  DESIGN 

winding  of  the  stator.     Any  filing  or  rough  treatment 
of  the  teeth  adds  very  largely  to  this  increased  loss. 

The  designer  has,  therefore,  to  fall  back  on  the  use 
of  total  loss  curves,  which  connect  the  sum  of  the 
hysteresis  and  eddy  current  losses  per  pound  of  plates 
with  the  induction,  at  some  fixed  frequency  and  thick- 
ness of  plates,  at  other  frequencies  the  assumption 
being  that  the  induction  may  be  varied  inversely  with 
the  frequency  for  the  same  total  loss  per  pound.  As 
these  curves  are  drawn  from  actual  measured  losses  in 
normal  machines,  they  may  be  relied  on  to  give  a  very 
fair  indication  of  the  losses  in  other  cases  where  the 
conditions  are  also  normal. 

At  50  cycles  per  second  and  plates  of  about  0*015" 
thick,  the  total  loss  at  an  induction  of  4000  lines  per  cm2, 
may  be  taken  at  about  one  watt  per  pound ;  the  loss 
about  doubling  at  7000,  and  again  doubling  to  4  watts 
per  pound  at  an  induction  of  10,000  lines  per  cm2. 

The  fact  that  the  induction  is  higher  in  the  teeth 
than  in  the  plates  at  the  back  of  the  slots  can  be  roughly 
allowed  for  in  calculating  the  weight  of  plates  by  not 
subtracting  the  weight  of  the  material  from  the  slots, 
i.e.  taking  the  weight  of  the  blanks  before  stamping  out 
the  slots.  This,  in  the  case  of  the  alternator  under 
consideration,  works  out  to  2440  pounds.  The  induction 
is  7700,  which,  on  the  above  scale,  corresponds  to  a 
loss  of  2*3  watts  per  pound,  making  a  total  of  5' 6 
KW.  or  adding  25  per  cent,  for  windage  and  friction, 
7  KW. 

The  magnet  current  for  1000  volts  at  375  r.p.m.  is 


EXAMPLE   OF  THE  DESIGN  OF  AN  ALTERNATOR     39 


23*25  amperes  on  open  circuit,  and  can  be  read  off  from 
the  curves  on  Fig.  12  for  other  loads. 

The  magnet  resistance,  allowing  a  temperature  of 
60°  C.,  is  2*5  ohms.  The  stator  resistance  per  phase, 
allowing  the  same  temperature  and  also  for  the  "  Field  " 
effect,  is  0*044  ohm. 


EFFICIENCY  AT  UNITY  POWER  FACTOR. 


At 

Core  loss  and  friction 
Sbator  C2R 
Rotor  C2R 
Sum  losses 
Output 
Input 
Efficiency 


Stator  C2R 
Rotor  C2R 
Sum  losses 
Input 
Efficiency 


\ 

\ 

i 

full 

1| 

l.J  load. 

7-0 

7-0 

7'0 

7-0 

7-0 

7-0 

0-17 

0-69 

1-54 

2-75 

4-3 

6-2 

1-44 

1-47 

1-6 

1-66 

1-76 

1-88 

8-61 

9-16 

10-14 

11-41 

13-06 

15-08 

62-5 

125-0 

187-5 

250-0 

312-5 

375-0 

71-11 

134-16 

197-64 

261-41 

325-56 

390-08 

87-9 

93-2 

94-9 

95-6 

96-0 

96-1  % 

AT  POWER  FACTOR  0-8. 


0-27 

1-08 

2-4 

4-3 

6-7 

9-7 

1-66 

1-99 

2-35 

2-75 

3-22 

3-75 

8-93 

10-07 

11-75 

14-05 

16-92 

20-45 

71-43 

135-07 

199-25 

264-05 

329-42 

395-45 

87-5 

92-5 

94-1 

94-7 

94-8 

94-8    % 

WEIGHTS  AND  COSTS  OF  ACTIVE  MATEBIAL. 


Stator  stampings 
Stator  winding 
Rotor  pole  pieces 
Rotor  pole  cores 
Rotor  winding 
Yoke  ring 


Material.                    Weight  in  Ibs.         Rate. 

Cost  £. 

M.S. 

2200 

30/-  cwt. 

29-5 

Cu 

520 

I/-  Ib. 

26-0 

W.I.  laminated 

300 

20/-  cwt. 

2-7 

C.S. 

900 

18/-  cwt. 

7-2 

Cu 

1030 

lOd.  Ib. 

43-0 

C.I. 

1600 

10/-  cwt. 

7-1 

£115-5 


In  general,  an  alternator  can  be  sold  at  a  profit  for 
four  times  the  cost  of  the  active  material  in  it,  in  this 
case  for,  say,  £460. 


CHAPTER  V 

SYNCHRONOUS    MACHINERY   IN    PARALLEL 

WHEN  a  synchronous  machine,  such  as  is  described  in 
the  last  chapter,  is  run  in  parallel  with  other  generators, 
there  are  one  or  two  problems  which  present  them- 
selves which  can  be  simply  solved  by  means  of  the  flux 
and  ampere  turn  diagrams  already  used. 

Let  us  assume  that  the  other  machinery  is  sufficiently 
large  and  powerful  to  maintain  constant,  or  practically 
constant,  voltage  on  the  common  bus  bars.  This  means 
that  the  stator  flux  of  the  machine  under  consideration 
is  fixed  and  is  not  therefore  altered  by  altering  the  rotor 
excitation ;  let  this  latter  be  set  at  the  value  obtained 
from  the  open  circuit  magnetization  curve,  to  give  the 
bus  bar  voltage,  and  let  sufficient  steam  be  admitted  to 
the  engine  driving  it  to  supply  the  friction  and  core 
losses.  The  alternator  will  now  neither  receive  nor  give 
power,  and  the  current  will,  of  course,  be  zero.  The 
magnet  poles  will  keep  exactly  in  the  centre  of  the 
revolving  stator  poles. 

Now  admit  more  steam  to  the  engine.  The  speed 
is  fixed  by  the  frequency  of  the  station ;  the  magnet 
poles  will  now,  however,  run  round  slightly  in  advance 
of  the  stator  poles.  This  is  the  condition  for  power  to 

40 


SYNCHRONOUS   MACHINERY  IN  PARALLEL         41 

be  given  by  the  alternator  to  the  bus  bars.  The 
amount  of  this  power  is  a  function  of  the  angle  by 
which  the  rotor  poles  lead  over  the  stator  poles,  and  is 
affected  solely  by  the  steam  pressure  behind  the  pistons 
of  the  engine. 

There  is  obviously  a  limit  to  the  possible  amount  by 
which  the  magnet  poles  can  lead  over  the  stator  poles  ; 
if  this  process  is  pushed  too  far  the  alternator  will  fall 
out  of  step. 

If,  instead  of  this,  the  steam  were  cut  off  and  the 
alternator  made  to  do  external  work  on  the  engine  or 
in  other  ways,  the  rotor  poles  would  be  held  back,  and 
whilst  still  running  the  same  number  of  revolutions  per 
minute,  would  lag  by  a  certain  angle  behind  the  stator 
poles.  The  machine  would  then  be  a  synchronous 
motor,  and  would  take  power  from  the  bus  bars.  If 
more  mechanical  resistance  were  offered  to  the  revolution 
of  the  motor,  the  angle  between  the  rotor  and  stator 
poles  would  be  increased  until  as  before  a  limit  was 
reached  and  the  motor  fell  out  of  synchronism. 

There  is  therefore  for  each  excitation  a  certain  angle 
forward  and  backward  from  the  mean  position  beyond 
which  the  magnet  pole  must  not  go.  For  an  engine 
which  has  not  a  uniform  turning  moment  throughout 
the  revolution  this  angle  becomes  interesting. 

The  condition  for  successful  running  is  that  the 
magnet  pole  shall  not  be  separated  from  the  stator  pole, 
supposing  the  latter  to  be  running  uniformly,  by  more 
than  a  certain  fraction  of  its  distance  from  the  next 
pole.  The  first  thing  to  be  noticed  is  that  this  condition 


42  ALTERNATING   CURRENT  DESIGN 

becomes  harder  to  satisfy  the  larger  the  number  of 
poles,  and  that  the  slow-running  prime  movers,  requiring 
therefore  the  largest  number  of  poles  for  a  given 
frequency,  are  the  gas  engines,  which  are  the  most  apt 
to  suffer  from  cyclic  irregularity,  and  that  for  the 
highest  speeds,  where  the  pole  pitch  is  very  large,  the 
turbines  are  almost  perfect  in  this  respect. 

The  cyclic  irregularity  of  an  engine  is  usually  stated 
by  its  makers  as  a  percentage  variation  in  speed 
throughout  the  revolution,  but  this,  before  it  can  be  of 
use  to  the  electrical  designer,  has  to  be  translated  into 
maximum  error  in  position  of  its  flywheel  expressed  in 
fractions  of  a  pole  pitch.  This  cannot  be  done  without 
knowing  the  number  of  impulses  received  per  minute, 
as  the  error  in  position  depends  on  for  how  long  the 
incorrect  speed  continues  in  the  same  direction.  For 
example,  suppose  a  10 -inch  pole  pitch  and  a  peripheral 
speed  of  5000  feet  per  minute  ;  let  us  say  that  the 
maximum  error  allowable  is  ^V  of  the  pole  pitch  from 
the  mean  position,  which  would  permit  a  total  dis- 
placement of  1  inch.  If  the  engine  were  running 
uniformly  only  to  within  1  in  300  in  speed,  the 
maximum  error  in  velocity  would  be  '3oo  of  500  feet 
per  minute,  or  200  inches  per  minute,  which  could  only 
be  allowed  to  continue  for  2~oo  of  a  minute  to  result 
in  1  inch  error;  i.e.  if  the  engine  ran  at  100  r.p.m.  it 
must  have  at  least  two  impulses  per  revolution  to  make 
the  time  between  the  impulses  200  minute. 

All  this  time  we  have  not  considered  the  excitation 
of  the  alternator.  Unlike  the  case  of  direct  current 


SYNCHRONOUS   MACHINERY  IN  PARALLEL         43 

generators  in  parallel,  the  excitation  is  powerless  to 
determine  which  alternator  shall  take  the  load,  or 
indeed  whether  a  particular  alternator  shall  run  as 
generator  or  motor ;  for  if  the  engine  were  tending  to 
run  faster  than  synchronism,  the  machine  would  generate 
with  a  very  weak  field,  or  if  there  was  a  mechanical 
resistance  to  its  turning  it  would  run  as  motor  with  a 
strong  field. 

Considering  any  group  of  alternating  current 
machinery,  generators  or  synchronous  motors,  running 
in  parallel,  they  jointly  require  a  certain  amount  of 
magnetizing  force,  and  this  can  be  supplied  by  all  or 
any,  generator  or  motor.  If  one  generator  or  motor  be 
over-excited  it  will  relieve  the  others  of  some  of  their 
magnetizing  work ;  the  medium  by  which  this  is 
transferred  being,  of  course,  the  phase  of  the  current  in 
respect  to  the  E.M.F. 

Take  the  case  of  a  synchronous  motor  driving  on  to 
a  steady  load  and  taking  power  from  constant  potential 
mains,  then  the  stator  flux,  the  speed  and  the  KW.  input 
are  all  fixed.  On  the  vector  diagram  (Fig.  13)  let  0V 
represent  the  stator  volts  and  likewise  the  stator  flux  to 
convenient  scales.  As  the  machine  is  acting  as  a  motor, 
the  current  will  in  the  main  oppose  the  voltage  ;  let  it  be 
represented  by  OC.  The  power  input  is  0V  X  OC  X  cos  <£, 
which,  being  fixed,  means  that  C  must  always  be  on  the 
line  AB.  The  stator  leakage  flux  OS  is,  as  before,  at 
right  angles  to  the  current,  and  the  air  space  flux  is  the 
resultant  of  this  and  the  stator  flux  0V,  namely  VS. 
Measure  along  SV  a  length  ST,  representing  the  ampere 


44 


ALTERNATING   CURRENT  DESIGN 


turns  obtained  from  the  synthesis  using  the  stator,  air 
space,  and  magnet  fluxes  as  before.  The  demagnetizing 
ampere  turns,  which  are  proportional  to  OC,  are  also  at 
right  angles  to  the  current ;  let  SB,  represent  them  on 
the  same  scale,  then  TR  represents  the  total  rotor 
excitation.  This  length  TR  is  the  thing  we  have 
control  of.  By  adjusting  the  excitation,  OC  can  be 
brought  into  line  with  0V,  when  the  power  factor  will 
become  unity  and  the  current  for  that  particular  load  on 


FIG.  13. 

the  motor  is  a  minimum,  as  are  also  the  lengths  of  OS 
and  SR. 

If  the  excitation  be  reduced  from  this  value  the 
current  OC  swings  to  the  other  side,  the  power  factor 
becomes  less  than  unity,  and  OS  and  SR  again  increase. 

When  C  is  toward  A  the  motor  is  magnetizing  for 
the  rest  of  the  circuit,  and  from  the  point  of  view  of  the 
generator  supplying  it,  takes  a  leading  current.  When 
C  is  toward  B  the  motor  is  only  partly  magnetized  by 
its  own  rotor  and  partly  by  the  alternating  current, 


SYNCHRONOUS  MACHINERY  IN  PARALLEL         45 

which  would  then  form  a  lagging  or  demagnetizing 
current  for  its  generator.  In  fact,  as  ampere  turns  are 
taken  off  the  motor's  magnets  they  have  to  be  put  on 
to  some  other  magnets,  or  the  voltage  of  the  system  will 
suffer. 

Just  the  same  reasoning  applies  if  the  machine, 
instead  of  being  a  motor  on  constant  load,  were  a 
generator  in  parallel  with  others  and  driven  by  an 
engine  with  fixed  steam  admission.  The  alternator 
could  be  made  to  do  more  or  less  of  its  share  of 
magnetization,  i.e.  give  a  lagging  or  leading  current,  by 
alteration  of  its  excitation. 


CHAPTER   VI 

COMPOUND  WOUND   ALTERNATORS 

IT  has  been  seen  that  it  is,  in  general,  the  inherent 
regulation  of  an  alternator  which  most  seriously  limits 
the  output  to  be  obtained  from  a  given  size  of  carcass ; 
the  heating  limit  can  usually  be  overcome  by  efficient 
ventilation,  and  space  can  generally  be  found  for  more 
copper  on  both  stator  and  rotor ;  also,  by  reason  of  the 
variation  of  voltage  caused  by  changes  of  current,  the 
full  load  output  has  frequently  to  be  fixed  below  that 
at  which  the  maximum  efficiency  occurs. 

The  direct  current  generator  meets  this  difficulty  by 
placing  an  additional  winding  on  the  magnets  in  series 
with  the  armature,  and  it  was  on  this  analogy  that  the 
first  attempts  were  made  to  effect  a  similar  result  in  the 
alternating  current  generator. 

The  problem  is,  however,  in  this  latter  case,  com- 
plicated by  two  different  difficulties,  the  first  being  that 
the  output  is  in  the  form  of  alternating  current,  and 
therefore  unsuitable  as  it  stands  for  energizing 
magnets  ;  and  secondly  that  the  voltage  drop  in  an  alter- 
nator, and  therefore  the  extra  magnetization  needed, 
depends,  not  only  on  the  amount  of  current,  but  also  on 
its  power  factor  ;  in  fact,  it  depends  much  more  on  the 

46 


COMPOUND    WOUND  ALTERNATORS  47 

power  factor  of  the  current  than  on  its  actual  amount  in 
amperes. 

There  are,  however,  some  classes  of  load  in  which 
the  power  factor  does  not  vary  much,  or,  better  still, 
improves  as  the  load  on  the  alternator  increases.  Such 
cases  can  be  dealt  with  by  the  simple  method  of 
rectifying  a  portion  of  the  main  current,  usually  by  a 
commutator  attached  to  the  alternator  itself,  and  by 
means  of  additional  slip  rings,  sending  this  rectified 
current  round  a  separate  winding  on  the  magnets 
exactly  like  the  direct  current  analogy.  The  com- 
mutator used  to  rectify  the  current  is,  however,  rather 
liable  to  give  rise  to  sparking  troubles,  which  can, 
nevertheless,  be  eliminated  by  careful  design  and 
adjustment. 

The  use  of  small  auxiliary  transformers  enables 
voltages  at  different  angles  to  be  combined,  and  the 
resultant  of  them,  after  passing  through  the  rectifying 
commutator,  employed  for  the  purposes  of  excitation. 
This  resultant  voltage  can  be  made  to  increase  either  as 
the  current  output  increases  or  as  the  power  factor 
decreases  ;  in  a  three-phrase  circuit,  for  instance,  the 
current  in  one  phase  and  the  voltage  across  two  phases 
are  at  an  increasing  angle  as  the  power  factor  decreases, 
and  therefore  the  resultant  will  increase  as  above,  and 
can  be  used  to  supply  the  additional  magnetization 
required  for  both  these  causes  of  the  voltage  drop. 

To  overcome  the  disadvantages  inherent  to  the  use 
of  rectifying  commutators,  and  also  the  complication  of 
two  separate  windings  on  the  magnets,  each  with  its 


48  ALTERNATING    CURRENT  DESIGN 

own  slip-rings,  a  method  has  been  developed  by  which 
the  alternating  current  output  is  made  to  increase  the 
voltage  of  the  exciter  itself,  and  thus  automatically  to 
increase  the  excitation. 

To  attain  this  end,  the  armature  winding  of  the 
exciter  is  provided  with  slip  rings  just  as  if  it  were  a 
rotary  converter,  the  number  of  poles  being  arranged  to 
give  the  same  frequency  as  the  main  alternator.  If 
now  these  slip  rings  are  fed  from  a  series  transformer 
in  the  feeder  circuit  there  will  be  produced  in  the  air 
space  of  the  exciter  a  magnetic  field  which,  if  the 
armature  were  stationary,  would  revolve  just  as  the  field 
of  an  induction  motor  revolves.  But  as  the  armature 
is  itself  revolving  at  the  same  speed  in  the  opposite 
direction,  this  field  is  really  stationary  in  space,  exactly 
like  the  field  produced  by  the  exciter's  own  magnets ;  if 
these  latter  are  capable  of  adjustment  by  turning  round 
on  their  own  bearings,  the  centres  of  the  two  sets  of 
poles  can  be  made  coincident  and  aiding  each  other ;  let 
this  be  so  only  when  the  power  facter  is  as  low  as  is 
likely  to  occur  in  practice,  for  that  particular  load.  If 
now  the  power  factor  improves,  the  current  will  reach 
its  maximum  earlier  in  point  of  time,  which  means  that 
the  resulting  pole  will  be  displaced  in  relation  to  the 
field  magnet  pole  of  the  exciter,  and  the  two  no  longer 
being  coincident,  the  result  will  be  a  weakening  of 
the  air  space  induction,  and  therefore,  of  the  exciter 
voltage. 

It  is  seen  that  the  conditions  for  automatic  voltage 
regulation  are  thus  fulfilled,  for  if  the  current  increases 


COMPOUND    WOUND  ALTERNATORS  49 

with  constant  power  factor  the  pole  strength  increases, 
the  pole  remaining  fixed,  whereas  if  the  power  factor 
decreases  with  constant  current,  the  pole,  whilst  remain- 
ing constant  in  strength,  is  moved  round  to  more  nearly 
coincide  with  the  field  pole,  and  so  the  effect  of  the  two 
is  increased. 

All  the  methods  hitherto  described  suffer  from  the 
defect  that  they  are  not  instantaneous  in  their  action. 
To  take  the  last  described  as  an  example,  although 
increased  magnetizing  force  is  applied  to  the  exciter 
directly  the  current  in  the  alternator  increases  or 
the  power  factor  decreases,  the  flux  through  the 
exciter  is  only  built  up  by  a  process  that  takes  time. 
When  this  flux  is  increased  the  exciter  voltage  is  indeed 
immediately  increased,  but  this  voltage  can  only  affect 
the  alternator  magnet  current  gradually,  which  in  its 
turn  can  only  raise  the  alternator  voltage  by  means  of 
the  comparatively  slow  increase  of  the  alternator  flux. 
On  the  other  side,  there  is  only  one  process  to  balance 
all  these,  i.e.  the  drop  in  terminal  voltage  does  not 
instantaneously  follow  the  increased  output,  but  only 
through  the  reduced  total  excitation  lessening  the 
alternator  flux. 

Processes  such  as  described  above  must  of  necessity 
be  slow,  because  the  force  producing  them  is  in  every 
instance  only  just  sufficient  to  give  the  required  result 
as  a  steady  condition,  the  exponential  term,  under  such 
conditions,  never  really  disappearing.  This  fact  is 
realized  by  such  devices  as  the  Entz  booster  and  the 
Tyrrell  regulator,  which  are  alike  in  applying  forces 

E 


So  ALTERNATING   CURRENT  DESIGN 

many  times  greater  than  those  finally  required,  and 
thus  accelerating  matters  by  making  the  whole  process 
merely  the  initial  stages  of  a  far  greater  change,  which 
however,  is  again  checked  as  the  required  result  is 
attained. 

There  are  other  methods  of  compounding  alternators 
which  aim  at  cutting  out  all  these  subsidiary  stages, 
and  making  the  armature  reaction  itself  counteract  its 
own  evil  effects.  One  of  these  methods,  due  to  Mr. 
Miles  Walker,  employs  rotor  poles  made  up  of  two 
parts,  magnetically  in  parallel.  The  magnet  winding  is 
wound  on  one  of  these  only,  which  in  consequence 
becomes  highly  saturated.  The  effect  of  the  armature 
reaction  is  to  weaken  one  pole  tip  and  to  strengthen  the 
other.  Things  are  so  arranged  that  the  one  to  be 
weakened  is  the  highly  saturated  part,  which  conse- 
quently is  not  much  affected,  whilst  the  other  un- 
saturated  pole  becomes  strengthened  and  adds  to  the 
total  flux,  and  therefore  to  the  voltage  of  the  machine. 
At  unity  power  factor  this  can  be  made  to  over-compound 
the  alternator,  the  voltage  actually  increasing  as  the 
current  increases,  but  the  effect  becomes  less  as  the 
power  factor  decreases. 


CHAPTER  VII 

INDUCTION    MOTORS — THEORY 

IN  the  synchronous  machines  dealt  with  in  the  last 
chapter  the  magnetization  of  the  circuit  was  obtained 
wholly  or  in  part  from  a  system  of  direct  current 
magnets.  As  we  have  seen,  this  gives  a  ready  method 
of  controlling  the  phase  relations  of  the  current  and  the 
E.M.F. 

The  power  factor,  however,  of  an  alternator  is  a 
function,  not  primarily  of  its  own,  but  of  the  circuit 
which  it  supplies  with  energy.  Induction  motors,  on 
the  other  hand,  derive  their  magnetization  from  the 
alternating  current  generators  from  which  they  are 
driven,  and  therefore  always  form  for  these  latter  a  load 
having  a  power  factor  less  than  unity,  lagging. 

It  is  of  the  utmost  importance,  from  all  points  of 
view,  that  this  magnetization  be  done  in  the  most 
efficient  way  possible — in  other  words,  that  the  power 
factor  of  the  induction  motor  should  be  as  high  as 
possible,  For  a  low  power  factor  not  only,  as  we  have 
seen,  affects  the  voltage  regulation  of  the  generators, 
their  heating  and  efficiency,  together  with  the  earning 
capacity  of  the  cables  connecting  the  two,  but  also  to  a 
still  greater  degree,  the  behaviour  of  the  motor  itself. 

5' 


52  ALTERNATING   CURRENT  DESIGN 

Compare  two  induction  motors  with  the  same  input  and 
therefore  with  approximately  the  same  cost  of  materials, 
the  one  with  a  maximum  power  factor  of  0*8,  the  other 
0*9.  The  latter  will  not  only  do  12|  per  cent,  more 
horse-power,  but  will  have  an  overload  capacity  of  more 
than  double  the  former's. 

These  facts  make  the  predetermination  of  power 
factor  of  preponderating  importance  in  the  design  of 
induction  machinery,  and  we  shall  therefore  examine 
into  this  question  at  some  length. 

Unlike  the  alternator,  the  induction  motor  starts 
with  a  certain  fixed  stator  flux  depending  only  on  the 
voltage  and  frequency  of  supply,  and  on  the  number  of 
turns  on  the  stator  winding ;  as  these  are  all  fixed 
quantities,  so  also  is  the  stator  flux. 

Now  it  is  only  that  portion  of  this  flux  which 
penetrates  into  the  rotor,  and  is  cut  by  the  rotor 
conductors,  which  is  used  in  the  production  of  brake 
horse-power,  so  that  any  leakage  of  lines  that  occurs  in 
the  process  must  be  taken  from  the  available  fixed 
supply,  and  the  problem  develops  into  a  study  of 
waste  fields. 

When  the  motor  is  running  light,  the  very  small 
stator  currents  drawn  from  the  supply  mains  are  only 
those  used  to  magnetize  the  circuit  and  to  cause 
sufficient  lines  to  flow  round  to  produce  a  counter 
E.M.F.  almost  equal  to  that  of  supply.  Under  these 
conditions  the  waste  field  is  very  small,  and  most  of  the 
stator  flux  finds  its  way  into  the  rotor.  But  as  an 
increasing  load  is  put  on,  the  rotor  conductors  lag  behind 


INDUCTION  MOTORS — THEORY  53 

the  revolving  field,  are  cut  by  it,  and  consequently 
have  current  induced  in  them ;  these  currents  tending 
to  oppose  the  magnetizing  currents  in  the  stator,  the 
latter  are  increased  proportionately  to  their  respective 
turns.  All  these  currents  give  rise  to  waste  fields, 
which  have  ultimately  to  be  supplied  from  the  stator 
flux. 

As  the  load  on  the  shaft  of  the  motor  increases  this 
process  continues,  until  by  the  increase  of  the  leakage 
fluxes  the  portion  penetrating  into  the  rotor  is  no  longer 
sufficient  to  provide  the  torque  demanded,  and  the  motor 
falls  out  of  step. 

The  various  leakage  fluxes  naturally  fall  under  three 
descriptions  :  there  is  the  true  slot  leakage,  i.e.  the  lines 
caused  by  the  magnetizing  power  of  the  currents  in  the 
slots,  and  which  jump  across  from  the  sides  of  the  teeth 
without  entering  the  air  space ;  there  is  a  somewhat 
similar  leakage  flux  round  the  conductors  forming  the 
end  connections.  These  are  not  helped  by  the  existence 
of  teeth,  and  so  have  most  of  their  path  in  air.  Their 
amount  depends  to  some  extent  on  whether  the  end 
connections  are  bound  down  on  to  an  iron  flange,  and 
also  on  the  way  in  which  the  end  connections  are 
grouped,  as  already  mentioned  in  considering  the 
analogous  case  of  an  alternator. 

These  two  leakage  fluxes  exist  in  both  stator  and 
rotor  separately,  but  there  is  a  third,  which  is  caused 
by  their  joint  action  on  the  opposite  sides  of  the  air 
space.  If  the  tooth  leakage  lines  be  drawn  coming  out 
from  the  tops  of  the  teeth  and  bending  round,  it  will 


54 


ALTERNATING   CURRENT  DESIGN 


be  seen  that  those  from  stator  and  rotor  will  combine, 
especially  when  the  tooth  of  one  is  opposite  the  slot  of 
the  other,  and  form  a  flux  which  zigzags  across  the  air 
space,  obtaining  its  magnetization  alternately  from 
stator  and  rotor  currents. 


FIG.  14. 

In  some  such  way  as  this  various  writers  have 
essayed  to  build  up  an  expression  for  the  total  waste 
field  in  terms  of  the  stator  flux.  This  fraction — total 
leakage  flux  over  total  stator  flux — is  usually  called  cr. 
Expressions  for  cr  generally  contain  three  terms  repre- 
senting the  three  sources  of  leakage,  viz.  zigzag,  slot, 
and  end  connections. 

Unfortunately,  the  calculation  of  waste  fields  from 
first  principles,  although  it  can  be  used  to  give  the 
general  form  to  the  expression,  is  too  difficult  and 
uncertain  to  rely  upon  solely  for  the  numerical  values  of 
the  constants  deduced,  which  latter  must  always  chiefly 
rest  on  empirical  authority.  With  these  remarks  we 
will  proceed  to  show  how  the  three  terms  of  such  an 
expression  for  cr  are  arrived  at. 


INDUCTION  MOTORS — THEORY  55 

In  a  two-pole  induction  motor,  let — 

N  be  the  number  of  slots  per  pole,  total. 
T  be  the  number  of  turns  in  series  per  phase. 
8   be   the  radial  clearance   between  stator  and 

rotor  in  cms. 

T  be  the  pole  pitch,  north  to  south,  in  cms. 
/   be   the  gross  length  of  plates,   exclusive  of 

ventilation  spaces,  in  cms. 
C  be  the  stator  current  in  R.M.S.  amperes. 
The  area  of  the  air  space,  allowing,  say,  15  per  cent, 
for  slot  openings,  is  0*85  . 1 .  T  cms2.,  and  its  length  8  cms. 

\/2CT 


The  maximum  ampere  turns  driving  the  flux  are- 

£t 

fer  the 
\ 


2 
Assuming  a  sine  wave  distribution  of  flux  over  the 


surface  of  the  pole,  the  maximum  induction  is  -  times 

the  average  ;  allowing,  say,  20  per  cent,  extra  magne- 
tizing force  for  the  iron  parts  of  the  magnetic  circuit, 
the  stator  flux  produced  is — 

X/2CT      0-85/r      2        1        0;4CTZr 
2xO'8X      8      X7TX172~        8~ 

For  the  zigzag  leakage  the   current   in   each   slot 
magnetizes  for  that  section.     The  current  per  slot  is 

3TC  T 

— *r-  .      The  area  of  the  path  of  the  lines  is  J  x  JT  x  ^, 

and  its  length  is  28. 

The  flux  produced  is  therefore  : — 

3\/2CT      1      T        I 
0-8N    X2XNX2S~     N28 


56  ALTERNATING   CURRENT  DESIGN 

This  expressed  as  a  fraction  of  the  stator  flux  above 
is  — 

CT/T        S         1'3  3 

SN2 


For  the  slot  leakage  from  the  sides  of  the  teeth 
a  figure  can  be  found  giving  the  lines  per  cm.  of  slot 
per  ampere  in  the  slot,  much  as  for  the  alternator 
already  discussed  ;  this  figure  is  in  the  neighbourhood 


of  1,  which  makes  the  slot  leakage  flux  3         _    or  as 

N 

a  fraction  of  the  stator  flux  — 

3>/2CTJ  8  108 

N        <  0-4CT/T  ~  sa7  NT 

The  end  connections  have  to  be  treated  in  much 
the  same  way.  Let  us  say  that  they  have  half  a  line 
per  ampere  per  cm.,  and  that  they  form  a  semicircle 
each  side  on  the  pole  pitch  as  diameter.  The  waste 
field  due  to  this  cause  will  be  then  \/2CT  x  TTT  x  0'5, 

58 
and  as  a  fraction  of  the  stator  flux,  -j~  • 

Gathering  together  these  three  terms,  we  may 
write 

3       108      58 


But,  as  before  stated,  the  whole  rests  on  an  entirely 
empirical  basis,  and  the  constants  must  be  made  to  fit 
the  experimental  results,  even  if  a  certain  amount  of 
violence  is  done  to  theoretical  basis  of  the  formula.  It 
is  only  as  the  expression  succeeds  in  interpreting  the 


INDUCTION  MOTORS — THEORY 


57 


results  of  past  work  that  it  has  any  claim  to  predetermine 
future  results. 

To  give  some  idea  of  how  the  three  terms  of  the 
expression  work  out  in  practice,  we  may  take  a  fairly 
typical  case,  where — 

N  =  12,  T  =  10,  8  =  0-1,  and  I  =  20 

~"*~  20 


Then 


144      120 
=  0-0208  +  0-0083  +  0'025 
=  0-054 

In  the  case  of  motors  having  squirrel-cage  rotors,  the 
last  term  is  usually  some  30  per  cent.  less. 


FIG.  15. 

Having  obtained  a  value  for  cr,  we  can  construct 
the  Heyland  diagram,  Fig.  15,  in  which  OB  represents 
the  total  stator  flux,  and  OA  the  leakage  flux  at  no 

OA 

load,  AB  being  therefore  the  rotor  flux  and  —  being 

cr.     At  any  other  load  the  leakage  flux  is,  to  the  same 
scale,  represented  by  OP  and  the  rotor  flux  by  PB,  where 


58  ALTERNATING   CURRENT  DESIGN 

P  is  any  point  on  the  semicircle  which  is  drawn  on  AB 
as  diameter.  As  P  moves  round  the  semicircle  from 
A  to  B  the  leakage  flux  is  seen  increasing  and  the  rotor 
flux  decreasing  until,  as  previously  stated,  the  motor 
has  not  sufficient  rotor  flux  to  maintain  the  load  and 
consequently  falls  out  of  step  and  stops,  in  which  case 
the  stator  flux  is  all  leakage  and  both  are  represented  by 
OB. 

Exactly  the  same  diagram  represents  the  currents  in 
the  motor.  OA  is  the  stator  current  on  no  load  to 
some  suitable  scale,  any  other  stator  current  being 
represented  by  OP  ;  this  becomes  equal  to  OB  when 
the  rotor  is  standing  and  short-circuited.  PA  is  pro- 
portional to  the  rotor  current,  the  actual  rotor  current 
being  obtained  by  multiplying  the  length  of  PA  by  the 
ratio — stator  turns  over  rotor  turns. 

The  direction  of  the  voltage  vector  is  0V  at  right 
angles  to  OAB,  so  that  the  cosine  of  the  angle  VOP  is 
the  power  factor,  and  the  maximum  value  this  can 
reach  is  when  OP  is  a  tangent  to  the  semicircle,  when 
it  follows  from  the  geometry  of  the  figure  that 

1  —  cr  1  —  cos  </>  max. 

cos  <f>  max.  =  1 — . —  or  cr  =  -—         -7— - 

1  +  cr  1  +  cos  <p  max. 

The  stator  current  at  no  load  is,  as  we  have  seen, 
the  magnetizing  current  required  to  drive  the  stator 
flux  through  the  magnetic  circuit,  and  as  such  is 
correctly  shown  at  right  angles  to  the  voltage ;  this 
magnetizing  current  is  always  the  resultant  of  the 
stator  and  rotor  currents.  If  all  the  data  are  known 
for  a  proposed  motor,  the  magnetizing  current  can  be 


INDUCTION  MOTORS — THEORY  59 

calculated,  as  also  can  or,  so  that  these  two  being 
known  the  Heyland  diagram  can  be  constructed  and 
the  whole  behaviour  of  the  motor  predicted  in  the 
manner  to  be  shown  later. 

By  making  a  few  assumptions  we  can  now  determine 
about  what  proportion  the  magnetizing  current  should 
bear  to  the  full-load  current.  Calling  the  no-load  current 
Co,  it  is  seen  from  the  diagram  that  AB  is  very  nearly 

equal  to  -- .     The  input  of  the  motor  is  E  x  OP  cos  <f> ; 

i  i  /•  r\-rt  i    •      A.13         Go 

the  maximum  value  of  Or  cos  <p  is  —  =  — . 

2j         Zcr 

If  the  motor  is  to  stand,  say,  100  per  cent,  overload 
without  coming  out  of  step,  the  full  load  is  half  the 
maximum  load.  Let  us  assume  the  efficiency  of  the 
motor  at  full  and  maxium  load  to  be  0'9  and  07 
respectively  and  the  power  factor  at  full  load  to 
be  0'9. 

The  maximum  input  is,  as  we  have  seen,  E  x  -— f  the 

2i(T 

maximum  output  is  07  of  this,  and  the  full-load  output 

half  of  the  maximum,  or  E  x  -  -  x  — .     With  a  full  load 

2i        ZiO~ 

efficiency  and  power  factor  both  0*9,  the  current  corre- 

-,.                      i  *  11  i    -j  •  07         1       Co  Co 

spending  to  normal  full  load  is —  x x  ^—  =  say,  — - 

2i          O'ol        *-iO~  0(7° 

In  the  case  we  were  considering,  where  cr  =  0*054, 
Co  is  0'27C,  and  in  practice  the  no-load  current  is 
usually  about  a  quarter  of  the  full-load  current. 

The  current  at  which  the  maximum  power  factor 
occurs  is,  by  the  geometry  of  the  Heyland  diagram,  equal 


60  ALTERNATING   CURRENT  DESIGN 

to  the  no-load  current  divided  by  \/o-.    For  this  to  agree 

with  C  =  — ,  cr  would  have  to  equal  0'04. 
ocr 

The  sort  of  limits  which  fix  the  output  of  an  in- 
duction motor  are  very  much  the  same  as  affect  the 
other  classes  of  electrical  machinery,  viz.  temperature 
rise,  overload  capacity,  and  efficiency,  with  power  factor 
thrown  in  to  make  it  more  difficult. 

As  was  the  case  with  alternators,  so  it  is  with 
induction  motors,  that  the  specific  loading,  expressed 
either  as  amperes  per  unit  of  circumference  or  ampere 
turns  per  unit  of  diameter,  should  not  exceed  certain 
limits.  In  the  case  under  consideration  the  limit  is 
somewhere  about  350  to  400  A.T.'s  per  cm.  of 
diameter,  corresponding  to  900  to  1000  A.T.'s  per  inch 
diameter. 

For  a  given  output  we  have  seen  that,  firstly,  the 
magnetizing  current  is  approximately  fixed  at  one-fourth 
of  the  full-load  current.  The  full-load  power  factor 
demanded  fixes  an  upper  limit  to  cr  which  keeps  both 
the  number  of  slots  per  pole  and  the  length  of  the 
motor  up,  whilst  questions  of  overload  capacity  and 
temperature  rise  both  limit  the  ampere  turns  per  cm. 
diameter. 


CHAPTER  VIII 

EXAMPLE  OF   THE  DESIGN  OF  AN   INDUCTION    MOTOR 

To  illustrate  the  preceding  theory,  we  will  take  the 
design  of  a  50-H.P.  induction  motor  to  the  following 
specification  :— 

Three  phase,  50  /-w,  500  volts,  wound  rotor.  Speed  750 
r.p.m.  on  no  load  and  not  less  than  725  r.p.m.  on  full 
load.  Efficiency  not  less  than  91  per  cent,  at  full  load, 
and  corresponding  power  factor  not  less  than  90  per 
cent. 

Temperature  rise  not  to  exceed  40°  C.  after  six 
hours  full  load.  The  motor  to  take  100  per  cent,  over- 
load momentarily  without  falling  out  of  step. 

The  full-load  current  per  phase,  at  the  above 
efficiency  and  power  factor,  is  53  amperes. 

For  a  full-load  power  factor  of  90,  the  maximum 
should  not  be  less  than,  say,  91,  and  for  this  or  equals 

°^9  =  0-047. 
1'91 

The  number  of  poles  is  eight. 

The  number  of  slots  per  pole  per  phase  should  be 
a  whole  number,  and  there  is  a  decided  prejudice  in 
favour  of  having  a  different  number  for  stator  and  rotor, 
which  course  will  be  followed  here,  although  facts  show 

61 


62  ALTERNATING   CURRENT  DESIGN 

that  there  is  very  little  against  having  the  same  number 
of  slots  in  stator  and  rotor  where  the  latter  is  wound. 

Three  slots  per  pole  per  phase  would  probably  make 
the  attainment  of  a  power  factor  of  90  per  cent,  difficult 
or  impossible,  so  try  4  and  5  for  stator  and  rotor,  equal 
to  12  and  15  per  pole  respectively.  This  brings  N,  the 
mean  of  stator  and  rotor,  to  13*5,  and  the  first  term  of 
the  &  expression  to  0*0164,  leaving  0*0306  for  the  other 
two  terms. 

A  clearance  of  one  millimetre  per  side  between  stator 
and  rotor  is  sufficient,  so  that  a  length  of  19  cms.  would 
make  the  third  term  0*0263.  The  middle  term  would 
then  be  satisfactory  with  a  pole  pitch  T  of  anything  over 
17  cms. 

It  now  becomes  a  question  of  adjusting  the  diameter 
to  obtain  a  suitable  figure  for  the  induction  in  the  air 
space,  which  should  be  somewhere  about  5000  lines  per 
cm2.  On  the  basis  of  400  ampere  turns  per  cm.  of 
diameter  and  a  length  of  19  cms.,  the  pole  pitch  of  17 
cms.,  necessitating  a  diameter  of  43*5  cms.,  would  give 
an  air  space  induction  of  about  6800,  allowing  15  per 
cent,  for  slot  openings.  On  the  above  assumptions  the 
air  space  induction  varies  inversely  as  the  square  of  the 
diameter,  so  for  B  5000,  the  diameter  would  be  about 
51  cms.  We  have  yet  to  see  if  this  fits  the  possible 
number  of  conductors  per  slot ;  the  total  turns  corre- 
sponding to  51  cms.  diameter  at  400  A.T.'s  per  cm.  are 
384,  which  divided  by  96,  the  number  of  stator  slots, 
makes  8  conductors  per  slot,  which  number  will  be 
satisfactory.  The  turns  per  phase  will  be  128  ;  if  the 


EXAMPLE   OF  DESIGN  OF  AN  INDUCTION  MOTOR     63 

diameter  is  made  50  cms.  the  A.T.'s  per  cm.  at  53 
amperes  will  be  407. 

The  full-load  stator  flux  is 

500  V!XWF_  xl* 

\/3      Sir  X  50  X  128 

This  contains  small  allowances  both  for  the  distributed 
nature  of  the  winding  and  for  the  volts  lost  in  its 
resistance,  which  two,  in  a  motor  of  this  size,  about 
balance  each  other. 

The  full  expression  for  cr  is  now 

3  10  X  O'l      ,5  x  O'l 


13-52+13'5  x  19-5  "*        19 

=  0-0164  +  0'0038  +  0'0263 
=  0-0465 
The  rotor  flux  =  1'02  x  (1  -  <r)  =  0'97  X  106. 

Take  the  air  space  flux  as  halfway  between  these, 
say,  1  x  106. 

The  19  cms.  of  plates  should  be  broken  up  into  four 
sections  with  1'5  cm.  ventilation  spaces  between  each, 
which  makes  the  length  between  end  plates  23  '5  cms. 
Taking  plates  0'015"  thick,  and  varnishing  both  sides  to 
0'017"  total  thickness,  the  net  length  of  iron  is  16*8  cms. 

For  the  maximum  induction  in  the  teeth  not  to 
exceed  17,000,  an  area  of  94  cms2,  is  required  ;  there  are 
12  teeth  per  pole,  each  tooth  therefore  must  be  0*47  cm. 
The  minimum  pitch  of  the  teeth  is  1*64  cms.,  leaving 
1'17  cms.,  say  11  mm.,  for  the  slot  width.  Winding  this 
with  round  wire  two  abreast,  lining  the  slot  with  a 
micanite  tube  1  mm.  thick,  and  covering  the  wire  with  a 


64  ALTERNATING   CURRENT  DESIGN 

cotton  braid  to  0*5  mm.  on  the  diameter  and  allowing 
1  mm.  margin,  leaves  3*5  mm.  for  the  diameter  of  each 
wire,  or  9*6  mm2,  area.  Two  of  these  in  parallel  will 
carry  53  amperes  at  a  density  of  2*75  amperes  per  mm2., 
which  is  quite  suitable. 

The  average  length  of  one  turn  made  up  of  two 
straight  pieces  23*5  cms.  long  each,  and  two  semicircles 
on  the  pole  pitch  of  21  cms.,  is  113  cms.,  which  makes 
the  resistance  of  the  128  turns  of  two  wires  in  parallel 
0'13  ohm  at  15°  C.,  or  0'15  ohm  at  60°  C.  The  loss  in 
the  three  phases  warm  will  be  1*26  KW.,  which  is 
about  3  per  cent,  of  the  input. 

There  will  be  8  wires  deep  in  the  slot,  which, 
allowing  2 '5  mm.  for  the  roof  and  1*5  mm.  for  margin, 
makes  38  mm.  depth  of  slot.  Leave  2  mm.  opening 
at  the  top  of  the  slot. 

The  double  depth  of  plate  behind  the  slot  for,  say, 
6000  lines  per  cm2,  would  be  10  cms.,  making  the 
outside  diameter  of  the  stator  plate  67 '6  cms.,  say, 
68  cms. 

In  the  rotor,  for  a  maximum  induction  of  17,000  in 
the  teeth,  an  area  of  89  cms2,  is  required.  There  are 
15  teeth  per  pole,  so  that  each  tooth  must  be  3 '6  mm. 
Assuming  a  depth  of  slot  of  25  mm.,  the  pitch  of  slots 
minimum  would  be  117,  which  leaves  8*1,  say  8  mm., 
for  the  slot. 

The  simplest  of  all  windings  is  two  bars  per  slot, 
which  would  give  40  turns  per  phase,  in  which  case 
the  volts  between  slip  rings  would  be  500  X  -f£s  =  156, 
which  is  quite  convenient. 


EXAMPLE   OF  DESIGN  OF  AN  INDUCTION  MOTOR     65 

For  a  first  approximation  the  rotor  current  may  be 
taken  as  equal  to  the  inphase  component  of  the  stator 
current  multiplied  by  the  ratio  of  the  turns,  in  this 
case  53  X  0*9  X  ^f  =  153  amperes.  Copper  to  carry 
this  at  3  amperes  per  mm2,  would  be  51  mm2,  The 
8  mm.  slot  will  take  a  5  mm.  wide  bar  by  10  mm.  deep, 
say.  Two  of  these  will  go  into  a  28  mm.  deep  slot. 
So  rotor  slots  are  120  —  28  X  8,  with  2  mm.  opening. 

The  average  length  of  one  turn  of  the  rotor  winding 
is  made  up  of  two  pieces  23*5  cms.  long  each  and  two 
end  connections  each,  say,  twice  the  pole  pitch  of 
18 '5  cms.,  making  121  cms.  total.  The  resistance  of 
40  turns  is  therefore  0'0165  ohm  cold  and  0*019  ohm 
warm.  The  total  loss  at  153  amperes  is  hence  1*34 
KW.,  or  3*4  per  cent,  of  the  input  to  the  rotor,  which 
will  make  the  full-load  speed  very  nearly  725  r.p.m. 

The  internal  diameter  of  the  rotor  plate  is  settled, 
in  this  case,  not  so  much  from  electrical  as  mechanical 
reasons,  which  call  for  a  depth  of  not  less  than  say 
i  cms.  a  side,  which  makes  the  hole  in  the  rotor  plate 
36  cms.  in  diameter,  the  corresponding  induction  being 
7000  lines  per  cm2. 

We  can  now  proceed  to  the  synthesis  of  the 
magnetizing  force  required.  The  areas  of  the  teeth 
will  be  taken,  as  for  the  alternator  already  described, 
one-fifth  of  the  way  from  the  smaller  end.  The  air 
space  area  will  be  the  mean  of  the  areas  of  the  roofs 
of  the  teeth  in  stator  and  rotor  plus  10  per  cent,  for 
spread. 

For  the  circuits  in  teeth  and  cores  the  net  length  of 

F 


66 


ALTERNATING   CURRENT  DESIGN 


iron  will  be  taken  16*8  cms.,  but  for  the  air  space  the 
length  of  the  assembled  plates — 19  cms. — is  used.  The 
length  of  the  path  in  the  plates  at  the  back  of  the 
teeth  is  taken  as  half  the  pole  pitch  at  the  mean 
diameter  plus  the  depth  of  the  plate. 

The  maximum  induction  in  teeth  and  air  space  is 

taken  as  -  times  the  average. 


With    these    explanations    the    synthesis    can 
tabulated  as  follows  : — 


be 


Length 
of  circuit 
cms. 

Area  of 
circuit 
cms-. 

Flux 
xios. 

B 

lines  per 
cm-,  max. 

H 
per  cm. 

HxZ 
C.G.S.  per 
2  poles. 

Stator  core  X  2 

17-5 

174 

1-02 

5,850 

1-5 

26 

Stator  teeth  i 

7-6 

119 

1-02 

13,500 

7'5 

57 

Air  space      

0-2 

353 

1-0 

4,450 

4,450 

890 

Rotor  teeth] 

5-6 

98 

0-97 

15,500 

15-0 

84 

Rotor  core  X  2 

12-0     I      138 

0-97 

7,000 

2-0 

24 

Total  C.G.S.  per  2  poles  =  1081 


Ampere  turns  per  pole  =    432 


Now,  this  magnetization  of  432  A.T.'s  is  derived 
from  all  the  three  phases.  For  the  alternator  it 
was  seen  that  the  demagnetizing  effect  of  these 

was  —  x  R.M.S.  current  per  phase  x  total  turns  per 

Zi 

pole  on  all  phases.    By  the  same  reasoning  the  magnetiz- 

432  x  2  X  8 
ing  current  per  phase  ot  this  motor  is  128  x  \/9  x  3 

=  12*8  amperes. 

The  value  of  this  no-load  current  from  the  approxi- 
mate expression  Co  =  C  x  5  x  cr  would  work  out  in 


EXAMPLE   OF  DESIGN  OF  AN  INDUCTION  MOTOR     67 

this  case  to  53  x  5  x  0'0465  =  12'3  amperes,  which 
shows  a  very  fair  agreement. 

The  static  current,  OB  on  the  Heyland  Diagram, 

12*8 

is  TTTrrTrrr  =  275  amperes.     We  now  have  all  the  data 
0*0465 

necessary  to  construct  the  diagram.  Nothing  further, 
however,  can  be  done  till  the  details  of  efficiency  are 
available. 

For  the  core  loss  take,  as  for  the  alternator,  the 
weight  of  plates  before  the  slots  are  cut  away,  in  this 
case  480  Ibs.  at  an  induction  of  5850,  which  is  pro- 
portional to  1*55  watts  per  pound  on  the  total  loss 
curve.  This  makes  075  KW.,  or  allowing  for  windage 
and  friction/say  1  KW. 

The  resistance  of  the  three  phases  of  the  stator 
winding  warm  is  0*45  ohm,  and  that  of  the  rotor 
0'057  ohm. 

If  the  diagram  be  drawn  on  some  good  squared 
paper,  and  a  scale  of  amperes  be  made  on  the  vertical 
edge,  certain  selected  stator  currents  can  be  set  off 
on  dividers  from  the  point  0,  and  pricked  off  where  the 
end  of  their  vector  would  touch  the  circle.  The  vertical 
heights  of  these  points  can  be  read  off  on  the  same 
scale  and  give  the  inphase  component  of  the  stator 
current ;  the  power  factor  is  obtained  by  dividing  the 
inphase  by  the  total  current  (Fig.  16). 

The  rotor  currents  are  proportional  to  the  length 
PA  (Fig.  15).  If  the  rotor  resistance  be  increased  by 
the  square  of  the  ratio  of  turns  in  stator  and  rotor 
respectively,  and  this  new  resistance  be  multiplied  by 


68 


ALTERNATING   CURRENT  DESIGN 


the  square  of  this  length,  to  the  same  scale  as  for  the 
stator  currents,  the  rotor  copper  loss  is  obtained. 
This  new  rotor  resistance  would  be,  in  this  case, 
0-057  X  (%«)2  =  0'58  ohm. 

The  square  of  the  stator  current  by  0'45  gives  the 
stator  copper  loss ;  adding  the  sum  of  these  to  the  core 
windage  and  friction  loss  gives  the  total  loss.  The 


\ 

iRo 

\ 

I 

160 

140 

^ 

*~ 

-T? 

5 

^ 

H 

^ 

• 

/ 

Xl 

0 

V- 

\ 

/\ 

'5 

s. 

/ 

\ 

80 

/' 

)0 

\ 

& 

\ 

60 

/ 

v 

/6 

\ 

'so 

\ 

/' 

0 

\ 

jfa 

) 

\ 

la 

I'5 

( 

> 

K 

)O 

An 
Pi 

ape 

a. 

res 

16 

• 

2C 

O 

3cx 

input  is  \/3  x  500  X  inphase  component  of  stator 
current.  The  output  is  this  minus  the  total  loss,  and 
the  brake  horse-power  is  the  output  divided  by  0746. 

The  slip  is  the  rotor  copper  loss  divided  by  this  loss 
plus  the  motor  output.  The  efficiency  of  the  motor 
output  over  input  for  each  current,  can  also  be  written 
down. 


EXAMPLE   OF  DESIGN  OF  AN  INDUCTION  MOTOR     69 


b  ** 

II 

l-e- 

t- 

if 

&.. 

f. 

W 

M 

1 

O 

ft 

>-4     25 

£8 

^ 

li 
li 

IS 

P3 

f 

I 
q 

I 

B 

1 

.2  « 

° 

£ 

*s 

0 

0> 

15 

7-0 

0-47 

o-i 

7-0 

0-03 

1-13 

6-08 

4-95 

6-6 

0-6 

81-5 

90 

14-0 

0-7 

0-18      14-0 

0-11 

1-29 

12-16 

10-87 

14-6 

1-0  \  89-4 

30 

25-5 

0-85 

0-4 

25-5 

0-38 

1-78 

22-0 

20-2 

27-0 

1-8 

91-9 

40 

35-5 

0-885 

0-72 

35-5 

0-73 

2-45 

30-7 

28-2 

37-9 

2-5 

92-0 

50 

45-0 

0-9 

1-12 

45-5 

1-2 

3-32 

39-0 

35-7 

47-9 

3-3 

91-5 

60 

54-5 

0-91 

1-62 

56-0 

1-82 

4-44 

47-4 

42-9 

57-4 

4-0 

90-6 

80 

72-5 

0-905 

2-87 

76-0 

3-34 

7-21 

63-0 

55-8    I    74-7 

5-7 

88-5 

100 

89-0 

0-89 

4-5 

95-0 

5-22 

10-7 

77-0    ;  66-3    i    88-8 

7-3 

86-1 

125 

106-0 

0-85 

7-0 

119-0 

8-2 

16-2 

92-0     75-8 

102-0 

9-8    82-4 

150 

120-0 

0-8 

10-2 

143-0 

11-9 

23-1 

104-0    :  80-9 

108-0 

12-9    78-0 

175 

129-0 

0-74 

13-8 

168-0 

16-4 

31-2 

112-0 

80-8 

108-0 

16-9 

72-0 

200 

132-0 

0-66 

18-0      190-0 

20-9 

39-9 

114-0 

74-1 

100-0 

22-0 

65-0 

These  results  are  plotted,  not  against  stator  current, 
but   against   B.H.P,     The  curves  will  then   show  the 


s6°KH 


i5°ht-H- 


.40 


± 


O     10     20     30     40     50     60     70     80     90     100    1 10    120    130    I4O    150 

B.H.P. 

FIG.  17. 

efficiency,  power  factor,  slip  and  stator  current  for  any 
particular  H.P. 


70  ALTERNATING   CURRENT  DESIGN 

From  these  curves  it  is  seen  that  for  50  B.H.P. 
the  stator  current  is  52  amperes,  the  efficiency  is  91*3, 
and  the  power  factor  90*3  per  cent.  The  full-load  slip 
is  3*4  per  cent.,  which  makes  the  full-load  speed 
725  r.p.m. 

The  curves  begin  to  bend  back  at  109  H.P.,  and  are 
commencing  to  show  instability  soon  after  100  H.P. 

The  power  factor  running  light  is  got  from  the 
fact  that  the  input  is  about  1*1  KW. — allowing  O'l 
KW.  for  stator  and  rotor  C2R  loss — whilst  the  imput 

inK.V.A.isX/3x500xl2-8=11>     The  power  factor 

1000 
is  therefore  about  10  per  cent. 

The  maximum  power  factor,  from  the  diagram,  is 
91  per  cent.,  and  occurs  at  a  stator  current  of  60 
amperes. 

The  efficiency  is  a  maximum  at  about  three-quarter 
load,  and  is  over  90  per  cent,  from  about  15  to  65  H.P. 

WEIGHTS  AND  COSTS  OF  ACTIVE  MATERIAL. 


Material. 

Weight  in  Ibs. 

Rate. 

Cost. 

Stator  plates 
Rotor  plates 
Stator  winding 
Botor  winding 

M.S. 
M.S. 
Cu 
Cu 

370 
190 
160 
140 

30/-  cwt. 
SO/-  cwt. 
I/-  Ib. 
I/-  Ib. 

£ 

4-95 
2-55 
8-0 
7-0 

Total  cost  of  active  material    £22-5 

As  for  the  alternator,  this  motor  would  probably  be 
sold  at  a  profit  for  four  times  this,  or  £90. 


CHAPTER  IX 

STATIC   TRANSFORMERS 

AFTER  the  study  of  generators  and  motors,  it  is  quite  in 
place  to  look  to  transformers. 

The  two  oldest  forms  of  static  transformers  are  the 
ring  of  iron  with  primary  and  secondary  windings 
wound  round  it,  and  the  induction  coil  with  a  single 
straight  core  with  both  windings  upon  it.  The  first  has 
given  rise  to  the  core  type  of  transformer,  but  now  has 
its  parts  rectangular ;  and  the  latter  to  the  shell  type, 
so  called  from  the  iron  which  completes  the  magnetic 
circuit  enclosing  the  windings. 

Consider  a  simple  transformer  of,  say,  the  core  type, 
with  two  windings  of  Tx  and  T2  turns  respectively, 
having  resistances  Rx  and  R2  ohms.  Call  the  ratio  of 
turns,  T!  over  T2  —  p. 

If,  the  secondary  winding  being  on  open  circuit,  an 
alternating  voltage  is  impressed  on  the  primary,  current 
will  flow  in  increasing  strength  until  its  magnetizing 
force  is  sufficient  to  drive  a  flux  through  the  iron  core, 
of  such  a  magnitude  that  the  voltage  induced  thereby 
in  the  Tx  turns  is  equal  to  the  impressed  voltage  less 
that  used  up  in  the  resistance — Ex — of  the  windings. 

71 


72  ALTERNATING   CURRENT  DESIGN 

This  current,  in  comparison  with  the  full-load  current, 
will  usually  be  very  small  indeed. 

A  voltage  corresponding  to  the  turns  and  the  flux 
threading  it  will  also  be  induced  in  the  secondary  coil. 

Any  current  taken  from  this  will  be  a  demagnetizing 
current,  and  the  primary  coil  will  therefore  take  an 
increase  of  current  in  the  ratio  of  the  turns  T2  to  T1?  so 
that  the  algebraic  sum  of  the  two  ampere  turns  will 
always  be  that  needed  to  magnetize  the  circuit. 

On  open  circuit,  the  ratio  of  the  secondary  voltage 
to  the  impressed  voltage  will  be  that  of  the  turns  T2  to 
TU  but  on  current  being  taken  from  the  secondary  its 
terminal  voltage  will  fall,  for  three  reasons  :  firstly,  due 
to  the  pressure  lost  in  sending  its  own  current  through 
the  resistance  of  its  own  windings  ;  secondly,  due  to  the 
flux  through  it  having  been  reduced  owing  to  the  corre- 

o  o  o 

spending  resistance  drop  on  the  primary  winding ;  and, 
thirdly,  due  to  the  fact  that  both  primary  and  secondary 
currents  set  up  leakage  fields  which  do  not  thread  the 
others'  coils. 

In  order  to  be  able  to  represent  the  effect  of  these 
leakage  fields  on  the  same  diagram  as  terminal  voltages 
and  volts  lost  in  resistance,  it  is  convenient  to  translate 
them  into  voltages  too,  remembering  that  really  the 
leakage  fluxes  combine  with  the  working  fluxes,  forming 
one  resultant  flux  which  produces  one  voltage  only  in 
each  coil. 

To  represent  both  primary  and  secondary  effects  on  the 
same  diagram  one  must  be  brought  to  terms  of  the  other. 
Let  A!  and  A2  be  the  primary  and  secondary  currents 


STATIC   TRANSFORMERS  73 

respectively.    The  current  Ax  in  the  resistance  Ej  causes 

a  drop  — — 1  at  the  secondary  terminals,  which  adds  to 

P 
the  secondary's  own  resistance  drop  of  R2A2. 

As  the  magnetizing  current  is  so  small  in  comparison 

with  the  load  currents,  we  may  write  Ax  =  — ;  so  that 

P 
the    total    drop    on    the    secondary   side   due    to    the 

resistances  of  both  windings  is  er  =  A.2lR2  H — 2l  J ;  this 

is  in  phase  with  the  current. 

The  reactance  voltage  drops  due  to  the  leakage 
fields  are  also  proportional  to  the  current,  but  at  right 
angles  to  it.  The  amount  of  the  waste  field  is  as  usual 
very  difficult  to  calculate,  as  the  leakage  paths  are  quite 
undefined.  The  total  drops  due  to  this  cause  can, 
however,  readily  be  measured  in  terms  of  the  secondary 
voltage  by  short-circuiting  the  primary  winding  and 
supplying  the  secondary  winding  with  sufficient  voltage 
to  cause  full-load  currents  to  circulate  in  both.  This 
applied  voltage  is  the  resultant  of  the  resistance  and 
reactance  voltages  at  right  angles  ;  the  former  is,  of 
course,  easily  calculated  from  the  measured  resistances, 
and  hence  the  reactance  drop  is  known. 

In  a  new  transformer  the  result  can  be  predicted 
from  the  data  obtained  from  somewhat  similar  ones  on 
test. 

On  power  factors  of  unity,  or  less  than  unity,  lagging, 
both  these  causes  reduce  the  secondary  voltage. 

Let,  in  Fig.  18,  E2  represent  the  secondary  terminal 


74  ALTERNATING   CURRENT  DESIGN 

voltage.  Draw  A2  to  represent  the  direction  of  the 
secondary  current  at  an  angle  </>  to  E2,  where  cos  <£  is 
the  power  factor  of  the  circuit  supplied  by  the  trans- 
former. In  the  same  straight  line  as  A2  draw  er  to 
represent  the  combined  primary  and  secondary  resist- 
ance drop,  to  the  same  scale  as  E2.  This  is  in  phase 
with  the  current.  At  right  angles  to  this  draw  est  to 
represent  the  combined  reactance  drop.  The  vector 


FIG.  18. 

joining  the  end  of  this  with  the  end  of  E2  is  propor- 
tional to  the  primary  terminal  voltage  and  equal  to  it  if 
multiplied  by  p. 

If  er  and  es  are  small  compared  with  Ej  and  E2,  then 
EX  —  E2  =  er  cos  <£  +  es  sin  <£  ;  that  is,  the  total  drop  of 
the  secondary  voltage  from  all  causes  is  er  cos  <f>  +  es 
sin  (f>.  This  is  seen,  by  the  geometry  of  the  figure,  to 
be  a  maximum  when  the  power  factor  of  the  circuit  is 

a 

such  that  tan  <>  =  -*. 


STATIC   TRANSFORMERS  75 

Before  leaving  this  diagram  it  is  interesting  to  note 
what  happens  if  the  power  factor  is  less  than  unity  but 
on  the  leading  side  of  E2.  In  this  case  it  is  seen  that, 
especially  if  the  magnetic  leakage  is  fairly  high,  the 
secondary  voltage  may  be  increased  instead  of  diminished 
as  the  load  increases,  and  still  more  so  if  the  current  tends 
to  lead  more  on  the  pressure  as  the  former  increases. 

This  fact  is  made  use  of  in  the  operation  of  rotary 
converters,  which  by  nature  of  the  odd  value  of  the 
alternating  voltage  required,  if  for  no  other  reason,  are 
practically  always  fed  through  transformers.  If  it  is 
remembered  that  a  rotary  is  essentially  a  synchronous 
motor,  and  the  paragraphs  at  the  end  of  Chapter  V. 
be  read  in  that  light,  it  is  seen  that  the  provision 
of  a  compound  winding  on  the  magnets  of  a  rotary 
converter  carrying  the  main  direct  current  pro- 
vides an  increasing  excitation,  and  therefore  a  power 
factor  tending  from  lagging  to  leading  as  the  load 
increases.  This  enables  the  transformer  feeding  it  to 
raise  its  secondary  voltage  although  itself  fed  from 
constant  potential  mains.  So  that,  although  the  rotary 
converter  operates  with  a  fixed  conversion  ratio  of  DC 
to  AC  volts,  the  net  result  is  that  the  addition  of  series 
turns  on  its  magnets  raises  the  voltage  on  the  direct 
current  side  with  increasing  load,  exactly  like  any 
other  over-compound-wound  D.C.  generator,  though 
really  from  a  very  different  cause.  If  necessary  the 
transformers  for  use  with  rotaries  are  made  with 
specially  large  magnetic  leakage  in  order  to  effect  this 
end. 


76  ALTERNATING   CURRENT  DESIGN 

The  voltage  regulation  of  transformers  may  be  made 
as  close  as  desired.  The  resistance  drop  is  a  question 
simply  of  quantity  of  copper  used,  and  the  reactance 
drop  one  of  sufficiently  interleaving  the  primary  and 
secondary  windings  so  that  the  lines  made  by  the  one 
are  bound  to  cut  the  other  also.  As  both  these  processes, 
however,  cost  money,  and  are  increasingly  expensive 
the  further  the  result  is  pushed,  it  is  worth  while 
to  consider  if  there  are  no  other  corresponding  dis- 
advantages. 

One  other  disadvantage,  besides  the  cost,  to  very  close 
voltage  regulation  is  the  difficulty,  when  running  such 
transformers  in  parallel,  of  ensuring  that  the  load 
divides  equally  between  them.  Take  the  case  of  two 
transformers,  one  having  a  9  and  the  other  a  10  per 
cent,  drop  ;  if  these  are  in  parallel  it  is  obvious  that 
they  must  have  the  same  secondary  voltage  and  there- 
fore the  same  drop,  say  9|  per  cent.,  when  one  will  be 
5  per  cent,  under-  and  the  other  5  per  cent,  over-loaded, 
which  is  not  of  much  consequence.  But  now  suppose 
that  the  regulation  of  the  two  is  2  and  3  per  cent, 
respectively,  and  say  2|  per  cent,  when  in  parallel,  one 
will  have  50  per  cent,  more  load  than  the  other,  the  one 
being  17  per  cent,  under-  and  the  other  25  per  cent, 
over-loaded. 

The  design  of  transformers  is  rendered  more  than 
usually  difficult  on  account  of  the  apparently  unlimited 
choice  which  is  offered  by  varying  the  relative  pro- 
portions of  the  iron  and  copper  used.  For  instance,  a 
100  V.  50  ^  transformer  might  have  one  turn  of  copper 


STATIC   TRANSFORMERS  77 

and  a  flux  of  45  million  lines,  or  a  million  turns  and 
45  lines  of  force.  Experience  has  shown,  however,  that 
there  exists  in  well- designed  transformers  a  fairly 
definite  ratio  between  the  flux  and  the  ampere  turns, 
though  the  value  of  this  ratio  naturally  depends 
somewhat  on  the  size  and  type. 

There  is  then  the  further  choice  of  the  lines  per 
square  centimetre  in  the  iron,  and  the  amperes  per 
square  centimetre  in  the  copper  ;  the  values  for  these 
are  largely  dictated  by  the  efficiency  aimed  at 
and  by  the  methods  employed  to  carry  off  the  heat 
generated ;  for,  whilst  in  small  apparatus,  natural 
cooling  may  be  sufficient  to  carry  off  the  heat  corre- 
sponding to  quite  a  moderate  efficiency,  yet  the  output 
increases  so  much  faster  than  the  linear  dimensions  that 
in  large  units,  even  where  quite  extraordinarily  high 
efficiencies  are  obtained,  some  artificial  method  of  cool- 
ing is  called  for  to  prevent  an  altogether  abnormal  rise 
of  temperature, 

This  artificial  cooling  may  take  the  form  of  a  blast 
of  air  forced  through  and  round  the  transformer  by  an 
auxiliary  fan,  or  again  the  whole  apparatus  may  be 
immersed  in  oil,  which  itself  may  be  cooled  either 
naturally  or  artificially.  The  former  method  is  cleaner 
and  in  some  ways  more  direct,  inspection  is  easier  and 
the  heat  generated  can  readily  be  led  out  of  the 
building  or  transformer  chamber. 

The  advantages  of  oil  cooling  are  that  the  air 
circulation  is  dependent  on  running  machinery,  which 
may  fail ;  the  air  may  be  damp  or  dust-laden.  Of  the 


78  ALTERNATING   CURRENT  DESIGN 

two,  the  fire  risk  with  air  is  greater  than  with  oil 
cooling.  In  very  high-tension  apparatus  static  dis- 
charges may  occur  in  air  which  combine  the  nitrogen 
and  oxygen  of  the  atmosphere,  forming  nitric  acid, 
which  deteriorates  the  insulation  and  corrodes  the 
copper.  Owing  to  the  larger  specific  heat  of  oil  the 
overload  capacity  is  greater  than  with  air  cooling,  and 
oil  is  a  very  good  insulator  by  itself  and  is  self-healing 
in  case  of  a  discharge  taking  place. 

The  material  used  for  the  electrical  circuits  is 
always  copper  having  a  fairly  constant  quality,  but  the 
magnetic  circuits  may  be  made  of  different  classes  of  iron 
or  of  various  alloys  of  iron  containing  small  proportions 
of  other  ingredients.  The  correct  proportions  of  iron 
and  copper  to  use  for  any  transformer  will  vary  with 
the  relative  cost  of  the  two  metals. 

Let     PC  be  the  price  of  copper  per  cubic  inch 
Pi  be  the  price  of  iron  per  cubic  inch 
I  be  the  length  of  the  core  in  inches 
d  be  the  diameter  of  the  core  in  inches 
t  be  the  depth  of  copper  a  side  in  inches 
A  be  the  amperes  per  square  inch 
and      B  be  the  lines  per  square  centimetre  ; 
Then,  neglecting  the  space  factors  for  both  iron  and 
copper,  which,  for  circular  coils  at  any  rate,  are  not  far 

different,  the  volume  of  the  iron  is  -  d*l,  and  that  of 

4 

the  copper  ir(d  +  t)lt,  and  the  total  cost  of  the  two 
will  be  these  expressions  multiplied  by  Pi  and  PC 
respectively. 


STATIC   TRANSFORMERS  79 


The  volts  in  a  coil  are  equal  to  the  flux  x  —/=•  X  10~8 

x  turns  in  the  coil.      The  flux  is  ^d2~B  x  6'45.     The 

output  W  =  volts  x  amperes.  The  ampere  turns  are 
/£A  and  the  amperes  this  divided  by  the  turns,  there- 
fore W=  d*R~  X  lt&  x  22'5  X  1CT8. 

Putting  this  expression  into  the  one  for  the  total 
cost,  we  have 

W  Pi          id  +  t 

Total  cost  =    A~ 


which  is  a  minimum  when 

t      1       /Pi 
PC 


This  gives  the  best  relation  between  the  depth  of 
copper  and  the  diameter  of  iron  core  when  the  ratio  of 
the  costs  of  iron  and  copper  is  known. 

For  iron  plates  at  20  shillings  a  cwt.  and  copper 
wire  at  a  shilling  a  Ib.  and  densities  7  '8  and  8  '9 
respectively,  PC  =  6  '4  Pi,  and  the  best  depth  is  when 

t  =  —  .      If,  however,   we    use    "stalloy"    at  twice  the 
o 

price  of  iron,  the  minimum  cost  occurs  when  t  = 


3'6 

Taking  the  first  value,  i.e.  that  the  depth  of  the 
copper  is  one-fifth  the  diameter  of  the  core,  and 
making  a  few  assumptions  such  as  that  the  length  of 
the  core  is  twice  its  diameter  and  that  B  =  7000 
lines  per  cm2,  and  A  =  1000  amperes  per  in2.,  the 
value  of  the  ratio — flux  to  ampere  turns — mentioned 


8o  ALTERNATING   CURRENT  DESIGN 

before  works  out  to  about  180  to  1,  which  is  actually 
very  near  the  figure  met  with  in  practice  ;  the  ampere 
turns  being  those  due  to  one  of  the  two  windings, 
not  both. 

The  expression  for  the  total  cost  shows  also  that 
this  is  proportional  to  the  output,  but  inversely 
proportional  to  the  induction,  the  density,  and  the 
frequency. 


CHAPTER   X 

EXAMPLE  OF  THE  DESIGN   OF   A  TRANSFORMER 

WITH  the  help  of  the  theory  discussed  in  the  last 
chapter  we  will  now  design  a  three-phase  350  KW. 
transformer  of  the  three  circular  core  type  with  common 
yoke.  Primary  voltage  2200,  secondary  415  volts, 
50^,  to  work  on  a  power  factor  of  0*85. 

The  secondary  full-load  current  corresponding  to 
412  K.V.A.  is  573  amperes,  and  at  98  per  cent,  efficiency 
the  primary  current  is  110  amperes,  both  star  connected. 

Taking  the  ratio  of  flux  to  ampere  turns  as  180  to 
1,  and  calling  the  secondary  turns  T2,  then 

415  x  v  2  x  108       1  573       T 

\/3        27r  x  50       T2 

and  T2  =  32*3,  say  32  turns  per  phase  in  4  coils  of  8 
turns  each. 

The  flux  will  be  3*4x  106  lines  in  each  core.  The 
area  for  this  at  B  =  7000  is  75  ins2,  using  plates  0*013" 
thick  and  varnished  to  0*015",  the  gross  area  is  86  ins2. 
This  may  be  made  up  of  two  blocks  11"  x  3"  and  two 
blocks  5j"  x  2",  which,  with  half  an  inch  ventilation 
spaces  between  each,  just  fit  into  a  circle  of  12f" 
diameter  and  give  88  ins2.,  the  net  area  of  iron  being 
77  ins2,  and  the  induction  6850  lines  per  cm2. 

8r  G 


82 


ALTERNATING   CURRENT  DESIGN 


The  low-tension  winding  at  1000  amperes  per  in2, 
requires  0*573  sq.  in. ;  wind  this  with  a  number  of  fairly 
small  square  conductors  in  parallel,  say  six,  each  •£§" 
square,  which  gives  0*585  in2,  and  980  amperes  per  in2. 
Cover  it  to  say  0*33 5"  with  double  cotton. 


IE! 

FIG.  19. 

Eight  turns  of  this  combined  conductor  would 
occupy  a  space  2"  x  2f  "  deep.  Allowing  |"  from  iron 
to  copper,  the  inside  turn  would  have  a  diameter  of 
13 75"  and  the  mean  diameter  of  the  coil  would  be  16'5';, 
making  the  mean  turn  52".  The  resistance  of  32  such 
turns  would  be  0*0019  ohm  per  phase,  and  the  total 
weight  on  three  phases  936  Ibs. 


EXAMPLE   OF  THE  DESIGN  OF  A    TRANSFORMER      83 

In  fixing  the  number  of  primary  turns,  allow  for 
420  secondary  volts,  or  5  volts  drop  ;  the  high  tension 


turns  are  then  32  x  —  —  =168.    The  density  should 

be  rather  lower  here  owing  to  the  additional  insulation. 
Two  conductors  J"  square  in  parallel  would  give  an 
area  of  0*125  in2,  and  a  density  of  880  amperes  per  in2. 
Cover  the  conductor  to  0*275"  and  wind  nine  layers  deep, 
or  2j".  The  three  coils  in  between  the  low-tension 
coils  can  then  have  10  conductors  side  by  side,  which  will 
take  up  2*75"  in  width,  leaving  two  coils  at  the  two  ends 
each  of  four  conductors  wide,  or  1*1". 

The  resistance  of  the  168  turns  is  0*0465  ohm  per 
phase,  and  the  total  weight  1048  Ibs. 

Allowing  1  in.  between  the  coils  and  at  each  end, 
the  length  of  the  windings  is  28*45",  so  make  the  iron 
core  30"  long. 

The  distance  between  centres  of  the  three  cores  is 
20*25",  made  up  of  1275"  for  the  iron,  5*5"  for  the  coils, 
and  2"  in  clearance  space.  The  total  length  of  the  yoke 
is  2  x  20*25"  +  11"  =  51*5".  The  area  of  the  yoke  is 
the  same  as  that  of  the  core,  and  is  similarly  arranged. 

The  total  weight  of  iron  is  4150  Ibs.,  the  maximum 
induction  6850  lines  per  cm2.  In  transformer  iron, 
partly  on  account  of  its  use  in  rectangular  sheets  with- 
out teeth,  and  partly  that  it  need  not  be  subjected  to  so 
much  ill  treatment  in  manufacture  as  are  core  plates  for 
alternators  or  motors,  the  loss  per  pound  at  similar 
inductions  is  much  less.  In  the  present  case  this  should 
not  exceed  0*7  watt  per  pound,  or  say  3  KW.  total. 


84  ALTERNATING   CURRENT  DESIGN 

The  copper  losses  warm  are  H.T.  1*9  KW.  and  L.T. 
2-1  KW.,  making  a  total  loss  at  full  load  of  7  KW.  in 
an  input  of  357,  or  a  full-load  efficiency  at  0*85  power 
factor  of  just  over  98  per  cent.  At  unity  power  factor 
the  total  loss  at  350  KW.'s  is  reduced  to  5'9  KW.,  and 
the  efficiency  works  out  to  98*3  per  cent. 

The  efficiencies  at  different  loads  are  shown  in  the 
following  columns  :— 

full         \l          l|load. 


Power  factor  0-85 

Iron  loss 

3-0 

3-0 

3-0 

3-0 

3-0 

3-0 

Copper  loss 

0-25 

1-0 

2-25 

4-0 

6-25 

9-0 

Total  loss 

3-25 

4-0 

5-25 

7'0 

9-25 

12-0 

Output 

87-5 

175-0 

262-5 

350-0 

437-5 

525-0 

Input 

90-75 

179-0 

267-75 

357-0 

446-75 

537-0 

Efficiency,  per  cent. 

96-4 

97-8 

98-0 

98-0 

97-9 

97-8 

Power  factor  unity 

Copper  loss 

0-18 

0-72 

1-62 

2-9 

4-53 

6-53 

Total  loss 

3-18 

3-75 

4-62 

5-9 

7-53 

9-53 

Input 

90-68 

178-72 

267-12 

355-9 

445-03 

534-53 

Efficiency,  per  cent. 

96-5 

97-9 

98-3 

98-3 

98-3 

98-2 

The  cost  of  active  material  is  :  for  plates,  4150  Ibs.  at 
205.  per  cwt.,  £37  ;  for  copper,  2000  Ibs.  at  Is.  per  lb., 
£100.  Total  cost  of  active  material,  £137. 

The  magnetizing  current  is  calculated  on  the 
assumption  that  each  phase  magnetizes  for  its  own  core 
and  the  yoke  halfway  to  the  next,  30"  and  20"  respec- 
tively in  length.  The  joints  at  each  end  of  the  core  are 
taken  as  equivalent  to  0*1  mm.  of  air. 

H  x  /  for  air  =  6850  x  0'02  =  137 

„    for  iron  =  2  x  127      =  254 

Total  391 

The  magnetizing  current  is  therefore  — 

391  x  0*8 

168  x  \/9=  1>3  -R"  M.S.  amperes  per  phase. 


EXAMPLE   OF   THE  DESIGN  OF  A    TRANSFORMER      85 


For  purposes  of  the  calculation  of  voltage  regulation, 
it  is  assumed  that  previous  experience  with  similar 
transformers  would  lead  one  to  expect  a  reactance  drop 
of  3  per  cent.  The  resistance  drop  in  the  secondary 
when  warm  is  0'0019  X  T15  X  573  =  1 '2 5  volts,  which 
is  0*52  per  cent,  in  the  star  voltage  of  240.  In  the 
primary  the  corresponding  figure  is  0*065  X  1*15  x 


o'4 


o'6 


Power  factor. 


0-9 


FIG.  20, 

110  =  5 '9  volts,  or  0'47  per  cent.     The  total  resistance 
drop  is  therefore,  say,  1  per  cent. 

The  total  voltage  drop  from  both  causes  is  then 
1  cos  (j>  4-  3  sin  </>,  where  cos  (/>  is  the  power  factor  of 
the  circuit  fed  from  the  secondary.  The  power  factor  at 
which  this  drop  is  a  maximum  is  when  tan  <£  =  3  or 
cos  (f)  =  0'32,  when  the  drop  is  3'16  per  cent. 


86 


ALTERNATING    CURRENT  DESIGN 


The  following  table  gives  the  total  drop  for  other 
values  of  the  power  factor  :— 


COB<£. 

$  in  degrees. 

Sin  $  X  3. 

Total  percentage  drop. 

1-0 

o-o 

o-o 

1-0 

0-95 

18-2 

0-93 

1-88 

0-85 

31-8 

1-58 

2-43 

0-6 

53-1 

2-4 

3-0 

0-4 

66-4 

2-75 

3-15 

0-2 

78-5 

2-94 

3-14 

o-o 

90-0 

3-0 

3-0 

CHAPTER  XI 

TRANSMISSION    LINES 

THERE  follows  naturally  from  generators,  motors  and 
transformers  the  question  of  transmission  of  electrical 
energy. 

Firstly  comes  the  question  as  to  what  system  of 
generating  electricity  is  best  adapted  for  its  transmis- 
sion. A  simple  comparison  can  be  made  of  the  various 
systems,  on  the  basis  of  equal  power  transmitted  for  a 
given  distance  with  a  given  loss,  the  pressure  at  the 
receiving  end  being  kept  the  same  for  all. 

For  the  sake  of  example,  take  100  KW.  delivered 
one  mile  away  with  a  10  per  cent,  loss,  the  pressure  at 
the  delivery  end  to  be  200  volts. 

Firstly,  on  the  direct- current  two- wire,  or  single- 
phase  two-wire  systems,  the  current  would  be 
500  amperes.  The  loss  in  each  line  is  5  KW.,  which 
requires  an  area  of  2*1  ins2,  of  copper  and  a  total  weight 
of  38  tons.  The  density  would  be  240  amperes 
per  in2. 

Secondly,  direct- current  or  single -phase  three  wires 
with  the  middle  wire  10  per  cent,  of  each  outer,  but  carry- 
ing no  current.  The  current  in  the  outers  is  250  amperes, 
the  loss  in  each  is  as  before,  5  KW.,  which  makes  the 

87 


88  ALTERNATING   CURRENT  DESIGN 

area  of  each  0'525  in2,  with  a  density  of  480  amperes 
per  in2.  The  total  weight  of  copper  is  10  tons. 

Thirdly,  two-phase  four  wires,  which  gives  the  same 
total  weight  as  for  a  single-phase,  38  tons. 

Fourthly,  two-phase  three-wires.  The  current  in 
each  outer  is  250  amperes  and  in  the  middle  wire  354. 
The  density  is  the  same  in  all  these,  i.e.  280  amperes 
per  in2.  The  area  of  each  outer  is  0*895  in2,  and 
of  the  middle  1*26  ins2.  The  total  weight  is  27 '6 
tons. 

Fifthly,  three-phase  mesh,  with  200  volts  between 
each  of  the  three  wires.  The  current  in  each  wire  is 
288  amperes,  the  area  1*05  ins2.,  the  density  274  amperes 
per  in2.,  and  the  total  weight  28*8  tons. 

Sixthly,  three-phase  star,  with  200  volts  between 
each  wire  and  the  star  point.  The  middle  wire  to  be 
10  per  cent,  of  each  of  the  outers,  but  carrying  no 
current.  The  total  weight  of  this  arrangement  is  9*8 
tons. 

Seventhly,  three-phase  star,  but  transforming  down 
to  200  volts  at  the  receiving  end.  The  voltage  to  be 
such  that  the  10  KW.  loss  is  combined  with  a  density 
of  1000  amperes  per  in2.  At  this  density  the  drop  is 
42  volts  per  mile  in  each  wire,  so  that  the  receiving 
voltage  must  be  420  star  volts,  or  730  volts  between 
lines,  and  803  volts  at  the  generator  end.  The  current 
per  line  is  79  amperes,  and  the  section  of  each  wire 
0*079  in2.  The  weight  of  the  three  wires  (the 
transformers  supply  the  middle  wire)  would  be  2*15 
tons. 


TRANSMISSION  LINES 


89 


Below  is  a  summary  of  these  results  : — 

1  MILE  TRANSMISSION. 
100  KW.'s  delivered  at  200  volts  with  10  KW.  loss. 


System. 

A  amperes 
per  cm-. 

Total  weight 
in  tons. 

Per  cent,  of 
D.C. 

1.  D.C.  or  single  phase      

240 

38-0 

100-0 

2.  D.C.  3  wires,       

480 

10-0 

27-0 

3.  2-phase,  4  wires  240 

38-0 

100-0 

4.  2-phase,  3  wires  280 

27'6 

73-0 

5.  3-phase,  mesh     274 

28-5 

75-0 

6.  3-phase,  star        

480 

9-8 

26-0 

7.  3-phase,  star,  with  transformers 

1000 

2-15 

5-7 

The  last  case  introduces  the  question  of  the  cheapest 
voltage  to  transmit  at,  because,  if  the  cables  be  covered, 
the  increased  cost  of  insulation  may  more  than  balance 
the  reduced  cost  of  copper. 

To  obtain  this  cheapest  voltage,  certain  assumptions 
have  to  be  made.  Few  manufacturers  will  guarantee 
their  cables  if  worked  at  more  than  1000  amperes  per 
in2,  on  account  of  temperature ;  this  is  not  a  very 
scientific  basis,  but  it  is  worth  while  to  see  what  results 
it  will  lead  to.  Another  basis  of  comparison  would  be 
equal  efficiencies,  which  can  be  expressed  as  equal 
percentage  pressure  drop  per  mile. 

In  general,  manufacturers'  catalogues  have  to  be  re- 
arranged in  order  that  the  cheapest  voltage  at  which  to 
transmit  a  given  load,  at  either  constant  density  or 
constant  efficiency  may  be  apparent. 

For  example,  let  us  assume  that  we  have  prices  for 
three-core  lead-covered  and  armoured  cables  for  three 
voltages  and  for  three  sizes  at  each  voltage,  as  under  :— 

Cables  of  0*01  in2,  area  per  core  insulated  for  1000, 


ALTERNATING   CURRENT  DESIGN 


6000,  and  10,000  volts  between  cores  and  to  the  sheath, 
<£215,  £310  and  £425  per  mile  respectively  ;  for  0'05  in2, 
per  core  for  the  same  voltages,  £450,  £550  and  £700  per 
mile  ;  and  for  O'l  in2.,  £720,  £825  and  £1000  per  mile. 
Plot  these  on  the  same  sheet  and  to  the  same 
horizontal  scale  of  £'s  per  mile,  one  vertical  scale  being 
volts  and  the  other  square  inches  area  per  core.  From  the 


Volts.     Square  inches. 
10,000 


,g 


5000 


TL 


I  ___ 


__  . 


-4 


K 


l I 


;£'s  per  mile. 

FIG.  21. 

constant  area  curves,  points  can  be  read  off  for  the  price 
curves  at  constant  volts  of  3500  and  8000. 

Now  the  area  of  each  core  of  a  three-core  cable 
delivering  KW.  kilowatts  at  E  volts  between  cores,  with 
a  loss  of  p  per  cent,  of  these  kilowatts  per  mile  trans- 
mitted, at  15°  C.  is— 

4224. 

— ins . 
P 


E2 


TRANSMISSION  LINES  91 

To  do  the  same  as  above,  but  at  a  density  of  A 
amperes  per  square  inch  instead  of  at  a  loss  of  p  per  cent., 
the  area  of  each  core  would  be  — 

KW      588  . 


v         .     2 
AA  =   ^-     —  ms2. 

The  areas  required  for  10,  50,  100,  500  and  1000 
kilowatts  at  a  loss  of  2  per  cent,  per  mile,  as  calculated 
by  the  above  expression,  are  as  follows  :  — 


KW.'s  at 

1,000 

3,500 

6,000 

8,000 

10,000  volts. 

10 

0-021 

0-00172 

0-00058 

0-00033 

0-00021  ins.2 

60 

0-105 

0-0086 

0-0029 

0-00165 

0-00105  „ 

100 

0-21 

0-0172 

0-0058 

0-0033 

0-0021 

500 

1-05 

0-086 

0-029 

0-0165 

0-0105 

1000 

2-1 

0-172 

0-058 

0-033 

0-021 

The  prices  of  these  read  from  the  price  curves  are  as 
follows  : — 


KW.'s  at 

1,000 

3,500 

6,000 

8,000 

10,000  volts. 

10 

280 

210 

255 



—    £. 

50 

750 

250 

275 

315 

360 

100 

— 

305 

285 

320 

370 

500 

— 

700 

430 

415 

430 

1000 

— 

— 

605 

515 

500 

These  are  plotted  on  Fig.  22. 

It  is  seen  from  this  that  each  load  has  a  cheapest 
voltage,  and  also  how  this  "  cheapest  voltage"  increases 
with  the  KW.'s  to  be  transmitted. 

If,  instead  of  the  loss,  the  density  were  kept  constant, 
a  similar  set  of  figures  would  be  obtained,  but  giving  a 
slightly  different  "  cheapest  voltage." 

Although,  with  the  exception  perhaps  of  telegraph 
wire,  the  material  almost  universally  used  for  electric 
conductors  is  copper,  there  are  other  metals  which 
have  certain  claims  for  consideration  as  possessing 
advantages  in  one  way  or  another  over  copper. 


92  ALTERNATING   CURRENT  DESIGN 

In  order  to  make  a  comparison,  one  must  be  sure 
of  the  basis  of  comparison  selected.  In  general  the 
problem  is  one  of  transmitting  a  certain  quantity  of 
electrical  energy  a  certain  distance  with  a  given  loss 
in  the  process  ;  thus  the  comparison  might  be  in  the 


IOOO 

£'s  per  mile. 


cost  of  a  conductor  one  mile  long  having  a  resistance  of 
one  ohm.  There  are  other  considerations,  of  course, 
besides  the  one  of  cost.  The  diameter  of  the  conductor 
is  important  as  affected  by  wind  and  snow.  The  weight 


TRANSMISSION  LINES  93 

of  the  conductor  has  a  direct  bearing  on  the  cost  of 
poles,  and  its  strength  must  be  considered  in  this 
connection,  in  relation  to  its  weight. 

For  the  solution  of  the  problem  as  stated  above,  four 
of  the  properties  of  the  material  of  the  conductor  must 
be  known,  namely,  its  specific  resistance,  its  density,  its 
tensile  strength,  and  its  cost  per  ton. 

If  p  be  the  specific  resistance  in  10~6  ohms  per  cm. 

length  per  cm2,  area  at  15°  C., 
and  8  be  the  density  in  grammes  per  cm3., 
S  be  the  tensile  strength  in  tons  per  in2., 
K  be  the  cost  in  £'s  per  ton, 
then  the  diameter  of  the  conductor  of  one  ohm  per  mile 

will  be  0'178\/p  inches. 

g 
The  weight  per  mile  will  be  *  tons,  and  the 

O*7    O 

.,    p  x  8  x  K  p, 

cost  per  mile  c £  s. 

39'3 

The  strength  of  the  conductor  considered  in  relation 
to  its  weight  may  be  expressed  as  the  number  of  miles 

of  itself  that  the  conductor  would  support  vertically ; 

n 
this  =  -£  very  nearly  indeed. 

In  the  table  on  next  page  are  given  a  few  of  the 
possible  metals  of  which  conductors  might  be  made,  with 
their  four  physical  properties  as  above,  from  which  are 
worked  out  the  particulars  of  the  one  ohm  per  mile 
conductor. 

It  should  be  noted  that  the  cost  given  is  for  the 
material  of  which  the  conductor  is  made,  and  does  not 


94 


ALTERNATING   CURRENT  DESIGN 


include  the  cost  of  making  it  into  a  wire  or  other 
suitable  form ;  for  instance,  sodium  would  probably 
have  to  be  contained  in  an  iron  tube. 


Conductor  1  mile  long 

„• 

§" 

a 
o 

§  - 

1  ohm  resistance  at  15°  C. 

*^ 

.§0 

JS 

c  55 

*£ 

p< 

92 

| 

Material. 

jr 

S 

tt! 

ft 

1 

| 

L 

2 

as 

'§ 

O.CC 

.3 

% 

42  o 

Cost. 

3 

0 

H 

5 

1 

I 

|f 

P 

8 

S 

K 

c 
i—  i 

! 

£ 

Aluminium    

2-84 

2-6 

15-0 

74 

0-3 

0-188 

5-8 

14 

Antimony      

37-0 

6-7 

0-4 

28 

1-08 

6-3 

0-06 

176 

Bismuth         

136-0 

9-8 

3-8 

896 

2-08 

34-0 

0-39 

30,500 

Brass,  Cu  f  Zn£ 

6-5 

8-4 

22-0 

48 

0-455 

1-39 

2-6 

67 

Bronze,  Cu,  Sn,  P  or  Si 

3-3 

8-9 

40-0 

69 

0-324 

0-75 

4-5 

52 

Cadmium       

10-6 

8-6 

5-2 

336 

0-58 

2-32 

0-6 

780 

Copper 

1-67 

8-9 

26-0 

59 

0-23 

0-38 

2-9 

22-4 

Gold    

2-32 

19-3 

17-5 

139,000 

0-271 

1-14 

0-9 

158,000 

Wrought  iron 

10-5 

7-8 

40-0 

6 

0-57 

2-09 

5-1 

12-5 

Cast  iron        

100-0 

7-2 

9-0 

3 

1-78 

18-3 

1-25 

55 

Lead   

21-0 

11-4 

1-4 

13 

0-82 

6-1 

0-12 

79 

Magnesium    

4-6 

1-7 

12-0 

672 

0-382 

0-2 

7-0 

134 

Mercury 

95-3 

13-6 

— 

250 

1-74 

33-0 

— 

8,250 

Nickel 

13-4 

8-9 

39-0 

171 

0-65 

3-04 

4-4 

520 

Platinum 

9-3 

21-5 

22-0 

238,000 

0-544 

5-1 

1-02 

1,220,000 

Silver  

1-56 

10-5 

19-0 

3,460 

0-222 

0-42 

1-8 

1,450 

Sodium          

5-2 

0-97 

0-01 

90 

0-406 

0-128 

0-01 

11-5 

Steel    

15-0 

7-8 

60-0 

5 

0-69 

3-0 

7-7 

15 

Tantalum       

16-5 

16-5 

27-0 

13,000 

0-725 

6-9 

1-6 

90,000 

Tin      

13-8 

7-3 

2-0 

157 

0-66 

2-56 

0-27 

40-5 

Tungsten       

10-7 

19-1 

11-0 

560 

0-58 

5-2 

0-58 

2,900 

Zinc    

6-1 

7-1 

3-4 

24 

0-44 

1-1 

0-48 

26-4 

Below  are  given  eight  of  the  more  interesting 
metals  arranged  in  order  of  merit  under  the  four 
different  counts.  For  the  sake  of  comparison,  copper 
has  been  taken  as  a  standard  and  called  one,  the  others 
being  compared  with  copper. 


TRANSMISSION  LINES 


95 


Size. 

Weight, 

Strength  (in  length  of 
itself  it  will  support). 

Cost. 

Silver               0-97 
Copper              1*0 
Aluminium      1'3 
Bronze              1'4 
Magnesium     1-66 
Sodium            1-76 
Wrought  iron  2-47 
Steel                3-0 

Sodium            0-34 
Aluminium      0-5 
Magnesium     0-53 
Copper             1-0 
Silver                1-1 
Bronze              2*0 
Wrought  iron  5-5 
Steel                7-9 

Steel               2-6 
Magnesium    2-4 
Aluminium     2-0 
Wrought  iron  1-8 
Bronze             1'5 
Copper             1-0 
Silver              0'6 
Sodium           0-003 

Sodium            0-52 
Wrought  iron  0'56 
Aluminium     0-63 
Steel                0-67 
Copper             1-0 
Bronze             2-3 
Magnesium     6-0 
Silver             65-0 

All  compared  for  a  conductor  of  equal  resistance  per 
mile. 

It  will  be  noticed  that  the  somewhat  curious  result 
is  arrived  at  that  sodium  forms  both  the  cheapest  and 
the  lightest  conductor,  whilst  aluminium  is  better  than 
copper  in  everything  but  size  ;  wrought  iron  and  steel 
are  cheap  and  strong,  but  very  heavy  and  large.  By  far 
the  most  costly  conductor  of  all  is  platinum,  although 
it  is  for  the  purpose  of  an  electrical  conductor  that  the 
largest  part  of  the  world's  output  of  platinum  is  used, 
namely,  in  the  manufacture  of  electric  lamps. 


CHAPTER  XII 

CHOKING   COILS 

IT  sometimes  happens  that  it  is  required  to  reduce  the 
amount  of  current  flowing  in  a  circuit.  In  direct- 
current  work  this  would  have  to  be  done  by  inserting  a 
series  resistance,  with  its  consequent  waste  of  energy  ;  a 
back  electro-motive  force  would  do  the  work  better  and 
more  economically,  but  is  difficult  to  arrange.  In  alter- 
nating-current work,  however,  a  method  exists  of  readily 
manufacturing  this  back  E.M.F  on  the  spot  in  the  piece 
of  apparatus  known  as  a  choking  coil. 

This  consists  of  a  magnetic  circuit,  either  wholly  of 
iron  or  partly  of  iron  and  partly  of  air,  round  which  is 
wound  the  conductor  carrying  the  main  current.  The 
current  flowing  round  the  iron  magnetizes  it,  thus 
causing  an  alternating  flux  to  flow,  this  in  its  turn  creates 
an  alternating  E.M.F.  in  the  conductors  encircling  it. 

Such  a  number  of  turns  is  wound  round  the  iron  as 
will,  multiplied  by  the  maximum  value  of  the  current, 
give  the  ampere  turns  needed  to  send  that  flux  round 
the  circuit  which  will  give  the  required  back  E.M.F. 

It  follows  from  the  principles  discussed  in  the  first 
chapter  of  this  book  that  this  back  E.M.F.  is  at  right 
angles  to  the  current. 

96 


CHOKING   COILS  97 

Suppose  that  it  is  required  to  work  a  50-volt 
10-ampere  arc  lamp  from  a  100-volt  circuit  ;  the 
current  of  an  arc  being  in  phase  with  the  voltage  across 
it,  the  choking  coil  voltage  is  at  right  angles  to  this 
latter,  the  supply  voltage  being  the  resultant  of  the 
two.  The  choking  coil  will  therefore  be  required  to 
give  a  voltage  equal  to  vToo2  —  502  or  86*5. 

Assuming  a  50  ^  circuit,  the  product  of  the  flux  and 


the  turns  will  equal  86'5  x_^  x  108  =  39  x  1Q6> 

2?r  X  50 

Taking  the  relation  established  for  a  transformer 
that  the  flux  should  be  of  the  order  of  90  times  the 
total  ampere  turns,  the  flux  would  be  187,000  lines 
and  the  turns  208. 

To  carry  these  lines  at  an  induction  of,  say,  10,000 
lines  per  cm2,  requires  2'9  ins2.,  or  say  2"  X  1*65", 
allowing  for  insulation  between  the  plates. 

Ten  amperes  at  1500  amperes  per  in2,  requires 
0*0067  in2.,  or  0*092"  diameter,  which  covered  to 
20  mils,  equals  0*112".  Winding  this  to  7  layers  and 
15  convolutions  per  layer  on  each  coil,  gives  a  coil 
0*8"  deep  and  1*8"  long.  The  inside  dimensions  of  the 
stamping  will  -be  2"  x  2"  and  the  outside  6"  x  6". 
The  yoke  piece  would,  of  course,  be  separate,  in  order  to 
slip  the  coils  over  the  two  limbs. 

The  mean  path  of  the  lines  in  the  iron  would  be 
14"  =  36  cms.  H  for  B  =  10,000  is  about  3,  making 
H  x  I  =  108  for  the  iron.  The  total  magnetizing 
force  of  the  two  coils  carrying  10  E.M.S.  amperes  is 

H 


98  ALTERNATING   CURRENT  DESIGN 

- — X          +  2Q8  =  3660,  which  leaves  3552,  which  can 
0*8 

be  used  up  in  the  air  space  between  the  removable  yoke 
and  the  two  limbs.  The  induction  in  this  air  space  is 
also  10,000,  which  means  0'055  cm.,  or  from  1|  to  2 
millimetres  a  side,  which  can  take  the  form  of  mica 
packing  and  is  readily  adjustable  to  obtain  the  exact 
back  E.M.F.  required. 

The  mean  turn  of  the  coil  is  about  11  inches,  so 
that  the  resistance  of  the  208  turns  is  0'23  ohm  cold, 
and  the  copper  loss  warm  with  10  amperes  is  26  watts. 

The  weight  of  the  iron  is  13  Ibs.,  which  at 
2  watts  per  pound  also  gives  a  loss  of  26  watts,  or 
52  watts  lost  in  all.  The  volt  ampere  input  to  the 
choking  coil  is  86*5  x  10  =  865,  from  which  the  power 
factor  is  0'06.  The  power  factor  of  the  whole  circuit 
consisting  of  arc  and  choking  coil  would  be  0*55,  the 
total  power  being  500  watts  for  the  arc  and  52  for  the 
coil,  and  the  input  being  1  K.V.A. 

In  the  continuous  current  analogy  a  series  resistance 
of  5  ohms  and  a  loss  of  500  watts,  or  nearly  ten  times 
as  much,  would  have  been  necessary. 

At  currents  less  than  10  amperes  the  back  E.M.F. 
of  the  choking  coil  will  be  sensibly  proportional  to  the 
current,  but  at  much  higher  currents  the  iron  will 
saturate  :  to  give  double  the  back  E.M.F.  would  require 
an  induction  of  20,000  lines  per  cm2.  H  would  then 
be  290,  making  H  x  I  for  the  iron  =  10,400,  and  7100 
for  the  air,  total  17,500  C.G.S.  units  or  48  amperes. 


CHAPTER  XIII 

ADDITIONAL    EXAMPLE    OF    THE   DESIGN   OF   AN 
ALTEENATOE 

THE  alternator  designed  in  Chapter  IV.  fulfils  the 
requirements  of  a  constant  pressure  generator  with  a 
good  inherent  regulation,  but  there  may  be  uses  for  an 
alternator  when  these  small  pressure  drops  are  out  of 
place.  For  instance,  in  the  case  of  an  alternator  for 
use  with  a  resistance  type  of  electric  furnace  it  is  more 
important  to  keep  the  KW.  input  to  the  furnace  as 
nearly  constant  as  possible  with  wide  variations  of  the 
resistance  offered  by  the  furnace.  This  means  that  as 
the  current  increases  the  voltage  should  decrease  in 
nearly  the  same  proportion. 

This  result  can  be  approached  by  the  use  of  a  large 
stator  reaction  combined  with  a  large  stator  leakage 
flux  ;  and  it  so  happens  that  both  these  tend  to  cheapen 
the  manufacturing  cost  per  KW. 

To  illustrate  this,  let  us  consider  the  design  of  a 
two -phase  alternator  for  furnace  work  giving,  say,  500 
K.V.A.  total,  at  130  volts  per  phase,  frequency  of  25, 
speed  100  r.p.m.,  30  poles. 

The  full-load  current  per  phase  will  be  1920 
amperes. 

99 


ioo  ALTERNATING   CURRENT  DESIGN 

A  stator  reaction  of  something  like  1500  ampere 
turns  per  inch  diameter  will  be  possible  ;  putting  this 
value  into  the  expression  in  Chapter  III.  gives  D2/ 
=  86,000,  which  for  a  length  of  about  10"  gives  a 
diameter  of  about  100  inches.  The  corresponding 
peripheral  speed  for  this  is  2600  feet  per  minute,  and 
the  pitch  of  the  poles  is  10' 5  inches.  All  these  figures 
are  quite  satisfactory. 

The  conductors  per  pole  per  phase  at  1500  total 
ampere  turns  per  inch  diameter  and  100  inches  diameter 
and  1920  amperes  per  phase  are  2*6.  Call  this  3; 
putting  each  conductor  in  a  tunnel  would  mean  6 
tunnels  per  pole,  or  180  total ;  the  pitch  of  the  teeth 
would  be  174". 

The  stator  conductor  for  a  density,  say,  of  2500 
amperes  per  in2,  would  be  077  in2. ;  this,  at  any  rate  for 
the  conductor  embedded  in  the  tunnel,  would  have  to  be 
stranded,  as  otherwise  the  "  Field  effect "  would  nearly 
double  the  RC2  loss  in  that  portion.  The  stranding 
will  increase  the  bulk  of  the  conductor  from  15  to  20 
per  cent,  for  the  same  conductivity. 

The  length  of  the  turn  on  the  stator  is  about  57  ins., 
which  would  make  the  resistance  of  the  45  turns  per 
phase  0*0022  ohm  cold,  the  lost  volts  warm  5,  the  total 
volts  per  phase  135,  and  the  stator  flux  27  X  106  lines 
per  pole. 

In  the  design  of  the  whole  magnetic  circuit  we 
must  allow  for  the  voltage  increasing  as  the  load  on  the 
alternator  falls,  in  order  to  keep  the  output  to  the 
furnace  as  nearly  constant  as  possible,  thus  the  induction 


ADDITIONAL  DESIGN  OF  AN  ALTERNATOR      101 

in  the  teeth  should  not  exceed,  say,  15,000  lines  per  cm2, 
at  full  load. 

In  a  two-phase  machine  the  pole  arc  should  not  be 
much  more  than  half  the  pole  pitch,  so  as  to  allow  of 
one  phase  being  entirely  out  of  the  field  at  one  time. 
To  do  this  in  this  case  allows  the  pole  a  width  of  3  teeth 
and  4  slots,  or  say,  6". 

The  net  length  of  iron  in  the  10"  length,  allow- 
ing for  three  |"  ventilation  spaces  and  plates  0*015" 
thick,  with  1  mil.  of  varnish  on  each  side,  is  7*5". 
The  teeth  are  then  0 '9 3"  wide,  leaving  0'  81"  for  each 
tunnel. 

The  copper  could  be  1*3"  x  0*7",  insulation  all  round 
with  0*05"  of,  say,  silesia  varnished  and  ironed  on  ;  the 
tunnels  could  then  be  1*5"  deep. 

The  iron  at  the  back  of  the  slots  for  an  induction  of 
say  12,500  would  be  2*25"  deep  each  side,  making  the 
outside  diameter  of  the  stator  plate  107 "5". 

The  stator  leakage  flux,  taking  for  tunnels  100  lines 
per  ampere  per  inch,  at  a  current  of  1920  amperes,  is 
27  x  106,  or  curiously  enough  exactly  equal  to  the 
stator  flux. 

It  is  safer  to  allow  for  a  power  factor  of  0*95,  which, 
however,  is  mostly  accounted  for  by  the  leads  and  not 
by  the  furnace  itself.  The  air  space  flux  at  this  angle 
by  the  vector  diagram  is  4*4  X  106.  The  rotor  leakage 
factor  is  probably  about  1*2,  so  that  the  rotor  flux  is 
5*3  x  106,  to  accommodate  which  in  cast  steel  at  16,000 
lines  per  cm2,  requires  51  ins2.  Make  the  pole,  say, 
10"  x  5"  and  assume  a  length  of  pole  of  6".  The  yoke 


itV&T&fY? 
-  *•**  s.'ft*.,  i« 

ALTERNATING   CURRENT  DESIGN 


102 


if  cast  steel  should  be  rather  more  than  half  this  area, 
say,  10"  X  3".     Take  the  radial  clearance  as  £". 

We  have  now  all  the  data  for  the  calculation  of  the 
full  load  magnetization,  which  works  out  as  follows  : — 

SYNTHESIS  AT  130  VOLTS,  1920  AMPEBES,  0-95  POWER  FACTOR. 


Length 
cms. 

Area 
cms2. 

Flux 

xio6. 

B                 H 

lines  cm2,     per  cm. 

HxZ 
C.G.S. 

Ampere 
turns  per 
pole. 

Stator  core    ... 
Teeth  
Air  space 
Magnets 
Yoke  

28-0 
7-6 
1-27 
30-0 
22-0 

217 

182 
387 
323 
387 

2-7 
2-7 
4-4 
5-3 
5-3 

12,500  !  6 
14,800  11 
11.400  11,400 
16,400  i  47 
13,700  ;  6-5 

168 
84 
14,480 
1,410 
143 

16,285 

6,500 

The  demagnetizing  ampere  turns  on  the  stator  are 

1920  x  45  x  2  x  \/2 

2       3Q  -=4100 

These  two  combined  on  the  vector  diagram  give  the 
rotor  ampere  turns  at  the  above  full  load  as  =  10,100. 

The  rotor  magnet  winding  may  very  well  take  the 
form  of  copper  strip  on  edge.  Exciting  from  100  volts 
and  allowing  36  inches  for  the  length  of  one  turn,  the 
area  for  10,100  ampere  turns  is  0*084  in2.,  say  1^" 
x  0*067".  This  would  carry  126  amperes  at  1500  amperes 
per  in2.  The  turns  would  be  80  per  pole.  Separating 
these  with  5  mil.  paper,  the  winding  would  occupy  5*85" 
radially  :  the  magnet  pole  should  be  6j"  long. 

The  resistance  cold  of  the  30  poles  in  series  is  0*69 
ohm,  the  loss  warm  12*6  KW.  or  2*5  per  cent,  of  500  KW. 

The  next  thing  required  is  the  open  circuit  magneti- 
zation curve.  Using  the  areas  and  lengths  of  the 


ADDITIONAL  DESIGN  OF  AN  ALTERNATOR      103 

magnetic  circuit  from  the  full-load  synthesis,  and  taking 
four  points,  this  works  out  as  follows  : — 


Line  volts  at  100  r.p.m. 

100 

150 

175 

200 

Stator  flux  X  106      ... 

2 

3 

3-5 

4 

B  and  H  Stator 
Teeth 
Air  

Magnets    ... 
Yoke 

9,200-3 
11,000-4 
5,200 
7,400-2 
6,200-1 

13,800-8-5 
16,500-28 
7,800 
11,200-5-5 
9,300-3 

16,200-23 
19,200-200 
9,100 
13,000-9 
10,800-5 

18,400-130 
22,000-650 
10,400 
14,800-18 
12,400-8 

H  x  I       Stator 
Teeth 
Air  

Magnets    .  .  . 
Yoke 

84 
30 
6,600 
60 
22 

238 
213 
9,900 
165 
66 

644 
1,520 
11,550 
270 
110 

3,640 
4,950 
13,200 
540 
176 

C.G.S.  per  2  poles    ... 

6,796 

10,582 

14,094 

22,506 

Ampere  turns  per  pole 

2,720 

4,240 

5,640 

9,000 

This  curve  is  drawn  on  Fig.  23  ;  from  it  is  found  that 
the  full-load  magnetization  would  give  204  volts  on 
open  circuit,  or  a  rise  of  57  per  cent. 

The  short  circuit  current  for  10,100  ampere  turns 
on  the  rotor  is  2500  amperes. 

We  have  now  three  points  on  the  load  curve  connect- 
ing volts  and  amperes  at  constant  speed,  power  factor, 
and  rotor  excitation — namely,  204  volts  0  amperes,  130 
volts  1920  amperes,  and  0  volts  2500  amperes.  Drawing 
through  these  points  the  best  curve  we  can  (Fig.  24),  it 
would  be  as  well  to  check  two  more  points,  say,  188 
volts  1000  amperes  and ^70  volts  2300  amperes;  these 


104  ALTERNATING   CURRENT  DESIGN 

Volts  per  phase. 


_L__ 


; 


2500  5000 

Ampere  turns  per  pole. 

FIG.  23. 


7500 


Volts  per  phase. 
300 


2000 

Amperes  per  phase. 

FIG.  24. 


3000 


ADDITIONAL  DESIGN  OF  AN  ALTERNATOR      105 

are  both  found  to  require  very  nearly  10,100   ampere 

turns  on  the  rotor. 

On  the  same  sheet  is  drawn  the  volt  ampere  curve 

for  500  K.Y.A.,  which  shows  that  for  voltages  between 

100  and  200,  the  two  curves  do  not  widely  differ. 

The    losses    at    full    load    are    approximately    as 

under- 
iron  loss,  2580  Ibs.  at  1-75  watts  per  Ib 4-5  KW. 

Stator  copper  =  2  X  0-0022  X  1-15  X  19202 18-6     „ 

Rotor  copper  =  0-69  X  1-15  X  1262     12-6     „ 

Total  loss 35-7    „ 

Output  =  500  X  0-95        475-0     „ 

Input          510-7     „ 

Efficiency 93  per  cent. 

This  rather  low  efficiency  is  not  so  much  due  to  the 
peculiarities  of  the  design  as  to  the  low  speed  for  the 
output,  necessitating  a  large  amount  of  active  material. 
The  weights  and  costs  of  active  material  are— 

Stator Iron  2,120  Ibs.  at  30s.  cwt.  £28-5 

Stator  copper  1,270      „       Is.  Ib.  63-5 

Rotor  poles  3,000      „       18s.  cwt.  24-0 

Rotor  copper  2,320      „       lOd.  Ib.  97-0 

Yoke  ring  2,170      „      18s.  cwt.  17'5 

10,880  Ibs.  £230-5 

This  could  probably  be  sold  at  a  profit  for  £900. 
If  this  is  compared  with  the  250  KW.  constant 
pressure  alternator  at  375  r.p.m.  and  0*8  power  factor, 
it  is  seen  to  be  about  one-third  the  cost  on  the  basis  of 
the  K.V.A.  at  one  r.p.m. 


CHAPTEK  XIV 

DESIGN    OF   A   SMALLER   TWO-PHASE    SQUIRREL-CAGE 
INDUCTION    MOTOR    AND    AUTO-STARTER 

THE  design  of  the  50  H.P.  wound-rotor  motor  described 
in  Chapter  VIII.  may  be  supplemented  by  that  of  a 
smaller  squirrel-cage  motor  ;  this,  of  course,  will  suffer 
from  the  disadvantages  of  such  a  rotor  winding  :  firstly, 
in  starting,  it  will  take  a  larger  current  from  the  mains, 
and  even  then  it  will  not  start  up  against  such  a  large 
load  in  comparison  with  its  rated  H.P.  ;  and  secondly,  it 
will  not  be  capable  of  speed  regulation  ;  it  will,  however, 
have  a  slightly  better  power  factor  than  the  corre- 
sponding wound-rotor  motor,  and  it  will  be  considerably 
cheaper  to  build  owing  both  to  the  simplicity  of  its 
rotor  winding,  and  to  the  absence  of  slip  rings  and 
brush  gear. 

For  the  sake  of  example,  let  us  take  a  5 -H.P.  motor 
to  work  from  a  50^w,  2-phase,  3-wire  circuit  at  220 
volts  per  phase.  Speed  light,  1500  r.p.m.,  i.e.  4  poles. 
The  motor  to  stand  50  per  cent,  overload  for  a  few 
minutes,  and  full  load  for  6  hours  with  a  temperature 
rise  of  not  more  than  40°  C. 

The  full  load  efficiency  of  such  a  motor  should  be 
about  85  per  cent,  and  the  power  factor  about  90  per 

106 


INDUCTION  MOTOR  AND  AUTO-STARTER         107 

cent.     The  current  per  phase  on  this  basis  is  about  11 
amperes. 

To  obtain  a  power   factor   of  90,   cr   would  =  ^-^ 

=  0-053. 

Take  for  a  first  approximation  4  slots  per  pole  per 
phase  in  the  stator,  making  8  per  pole  and  32  total. 
The  rotor  slot  number  should  be  as  dissimilar  as 
possible  from  this,  and  also  as  high  as  practicable ; 
try  45. 

N  in  the  cr  formula  would  then  be  9*6  and  the  first 
term  0*0325.  S,  the  radial  clearance,  could  be  as  low, 
with  good  mechanical  workmanship,  as  0*5  mm. 
Making  the  length  12  cms.  and  taking  advantage  of 
the  30  per  cent,  decrease  in  the  third  term  of  the  cr 
expression  due  to  the  squirrel-cage  winding,  the  value 
of  o-  =  0*053  would  be  satisfied  with  a  pole  pitch  of 
anything  over  9  cms. 

Taking  300  ampere  turns  per  cm.  diameter,  with  11 
amperes  per  phase  and  9  cms.  pole  pitch,  the  air  space 
induction  would  work  out  to  about  10,800  ;  reducing 
this  to  5000  would  give  pole  pitch  of  13*2  and  a 
diameter  at  the  air  space  of  17  cms.  nearly. 

On  the  foregoing  assumptions  the  total  turns  for  17 
cms.  diameter  are  464,  which  is  29  conductors  in  each 
of  the  32  slots,  making  232  turns  per  phase. 

To  carry  11  amperes  at  about  4  amperes  per  mm2, 
requires  275  mm2.  No.  15  S.W.Gr.  is  2*63  mm2,  area, 
which  would  make  the  density  4*2. 

The  average  length  of  a  turn  on  the  stator  would  be 


io8  ALTERNATING   CURRENT  DESIGN 

about  68   cms.,  the  resistance   per  phase  cold  would 
therefore  be  1  ohm,  or  about  13  volts  lost,  warm. 

The  total  flux  per  pole  in  the  stator  will  be  0*42  x 
106  lines. 

3  10  x  0-05       3;5  X  CK)5 

-+9^TxT3:4H  12 


=  0-051 

which  makes  the  rotor  flux  0'4  x  106. 

The  12  cms.  length  will  have  one  ventilation  space 
1  cm.  wide,  and  will  have  a  net  length  of  iron  of  10  '6 
cms. 

The  width  of  each  tooth  for  the  induction  never  to 
exceed  17,000  lines  per  cm2,  will  be  4  '6  mm.,  which 
makes  the  slot  12  mm.  wide.  Insulating  this  with  0*5 
mm.  a  side,  leaving  O'o  mm.  margin,  and  insulating  the 
wire  to  0*25  mm.  on  its  diameter  with,  say,  varnished 
silk,  5  wires  will  go  in  abreast.  The  overall  depth  of 
the  slot  will  therefore  be  about  17  mm.  with  a  2  mm. 
opening. 

The  radial  depth  of  iron  at  the  back  of  the  stator 
slots  for,  say,  B  =  7000  is  2*8  cms.,  making  the  outside 
diameter  of  the  stator  plate  26  cms. 

The  rotor  copper  per  slot  for  a  density  of  about  5 
amperes  per  mm2,  is  approximately 

32  x  29  x  2'63      4'2 

x        =  46  mm2. 
45  5 

This,  in  a  round  bar,  has  a  diameter  of  7*6  mm., 
which  would  go  through  a  hole  in  the  rotor  plate  of 
8  mm.  diameter,  no  insulation  being  necessary.  The 


INDUCTION  MOTOR  AND  AUTO-STARTER 


109 


minimum  width  of  tooth  would  then  be  3 '4  mm.,  which 
is  ample  to  carry  the  flux.  The  rotor  plate  could  have 
a  hole  in  its  centre  up  to  1 1  "5  cms.  in  diameter  for  the 
induction  not  to  be  over  10,000  lines  per  cm2. 

The  end  ring  should  have  a  cross-sectional  area  of  a 
little  less  than  half  the  rotor  bars  per  pole,  in  this  case 
about  15  mm.  square. 

The  synthesis  of  the  magnetic  circuit  works  out  as 
follows  : — 


Length. 

Area.            Flux. 

B. 

H. 

HxZ. 

Stator  core  X  2  ... 

12-3 

60 

0-42 

7,000 

2 

25 

Stator  teeth 

3-4 

46 

0-42 

14,400 

10 

34 

Air            

0-1 

150 

0-41 

4,300 

4300 

430 

Rotor  teeth 

1-6 

42 

0-4       i  15,000 

12 

19 

Kotor  core  X  2   ...         7'2 

40 

0-4         10,000 

3 

22 

Total  C.G.S.  per  2  poles        530 
Ampere  turns  per  pole       212 


From   this   the  magnetizing  current  per  phase  is 

212  x  4X2 
\/2  x  2  x  232 


212  x  4  x  2 

Toon  =  2'6  amperes. 


The  static  current  is  this  divided  by  cr  =  51  amperes. 
The  Heyland  diagram  (Fig.  25)  is  drawn  from  these 
two  currents. 

The  stator  iron  loss  is  approximately  given  by  55 
Ibs.  of  iron  at  2  watts  per  pound  =  110  watts  ;  add  to 
this  30  watts  for  windage  and  friction  and  the  fixed  loss 
becomes  140  watts. 

For  the  squirrel-cage  rotor  loss,  the  best  we  can  do 
is  to  say  that  from  actual  data  on  similar  motors  the 


no 


ALTERNATING   CURRENT  DESIGN 


full  load  slip  will  be  about  5  per  cent.,  which  gives  a 
rotor  C2R  loss  at  full  load  of  about  200  watts. 


Amps. 

35 

^  ' 

8T 

—  -, 

>f 

x^ 

>o 

s> 

X 

/ 

s,, 

/ 

\ 

/ 

6 

\ 

1 

\ 

/ 

\ 

\ 

/a 

\ 

5 

s 

\ 

3 

_ 

\ 

25 


FIG.  25. 


75 


With  the  help  of  the  Hey  land  diagram  we  can 
now  work  out  the  whole  behaviour  of  the  motor  as 
under  :  — 


ti 

tf 

1      rt 

| 

^ 

11 

Jl 

|| 

6 
S 

111'  ? 

1 

I 

1 

0* 

W 

£3 

•§  s 

oo  i 

•*! 

1 

rg  s 

I 

" 

o 

PQ 

02 

^ 

3 

1-5 

0-5  !   21 

1-5     4 

165 

660 

495 

0-7 

0-8 

75-0 

5 

4-0 

0-8  !   58 

4-0    32 

230 

1760 

1530 

2-1 

2-0 

87-0 

8 

7-0 

0-88  i  148 

7-0    98 

386 

3080 

2694 

3-6 

3-5 

87-5 

11 

9-9 

0-9    280 

10-0   200 

620 

4360 

3740 

5-0 

5-1 

86-0 

16 

14-2 

0-87   590 

15-0   450 

1180 

6200 

5020 

6-7 

8-2 

81-0 

25 

20-5 

0-82  1440 

23-5  1100 

2680 

9000 

6320 

8-5 

14-8 

70-0 

30 

23-0 

0-77 

2070 

28-5  1620 

3830 

10200 

6370 

8-5 

20-0 

63-0 

35 

24-0 

0-69  2840 

33-0  2170 

5150 

10600 

5450 

7-3  28-0 

51-0 

These  are  plotted  on  Fig.  26. 

For  the  power  factor  running  light  the  losses  are 
140  +  16  for  C2R  =  156  ;  the  volt-ampere  input  is 
2  x  220  X  2*6  =  1140,  which  makes  the  power  factor 
about  14  per  cent. 


Per  cent, 
and  amps. 


INDUCTION  MOTOR  AND  AUTO-STARTER 

WEIGHTS  AND  COSTS  OF  ACTIVE  MATEBIAL. 


in 


Stator  plates 
Rotor  plates 
Stator  copper 
Rotor  copper 


43  Ibs.  at  30s.  cwt. 
18   „    at  30s.  cwt. 
16   „    at  Is.  Ib. 
10   „    at  9d.  Ib. 


£0'58 
0-24 
0-8 
0'38 


90 


So 


60 


P.f 


B.H.P? 


FIG.  26. 


Auto-starter  for  the  above  motor. 
To  prevent  the  undue  rush  of  current  which  would 
result  from  switching  the  stator  of  such  a  motor  straight 
on  to  the  mains  an  "  auto-starter  "  is  employed.  This 
device  performs  two  functions,  firstly,  it  causes  a  reduced 
voltage  to  be  applied  to  the  motor  when  starting  up, 


H2  ALTERNATING   CURRENT  DESIGN 

which  consequently  reduces  the  current  sent  into  the 
motor ;  and,  secondly,  by  doing  this  by  means  of  a 
transformer,  the  actual  current  demanded  from  the 
mains  is  less  than  the  current  sent  into  the  motor 
by  nearly  the  same  proportion  in  which  the  voltage  on 
the  motor  is  reduced  from  that  of  the  mains. 

If  a  coil  of  wire  is  wound  round  an  iron  core  and  an 
alternating  voltage  applied  at  its  ends,  the  voltage  will 
be  divided  up  proportionately  to  the  turns,  i.e.  a  point 
halfway  along  the  coil  will  give  half  the  line  voltage 
from  that  point  to  either  end  of  the  coil ;  but  not  only 
this  but  the  half  number  of  turns  will  act  in  every  way 
as  the  secondary  windings  of  a  transformer  on  the  same 
core,  and,  neglecting  the  small  loss  in  the  core  and  winding, 
will  deliver  the  same  volt  amperes  as  are  supplied  by  the 
mains,  giving  a  greater  current  as  the  voltage  is  reduced. 

This  is  just  what  is  wanted  for  the  starting  up  of  a 
squirrel-cage  induction  motor.  A  suitable  switch  will 
apply  consecutively  higher  voltages  to  the  motor  as  its 
speed  increases,  finally  leaving  the  motor  straight  on  to 
the  mains  with  the  auto- transformer  coil  switched  off. 

The  two  phases  must,  of  course,  be  wound  on 
separate  iron  cores,  but  can  share  a  common  yoke  like 
the  three-phase  transformer,  but  unlike  this,  must  have 
an  iron  circuit  to  take  the  resultant  flux,  which  in  the 
two-phase  case  is  \/2  times  the  flux  of  each  phase, 
whilst  in  the  three-phase  case  the  resultant  flux,  of 
course,  vanishes. 

In  the  case  under  review  the  voltage  per  core  is  220 
and  the  frequency  50.  If  the  motor  is  tapped  on  to  the 


INDUCTION  MOTOR   AND  AUTO-STARTER          113 

middle  of  the  winding,  each  half  will  contribute  current 
equally,  so  that  if  we  wind  with  a  conductor  which  will 
carry  the  full-load  current  of  the  motor  at,  say,  5  amperes 
per  mm2.,  it  will  enable  the  motor  to  have  two  or  three 
times  its  normal  current  whilst  starting  up  with  safety. 

Eleven  amperes  at  5  amperes  per  mm2,  requires 
2-2  mm2 ;  16's  S.W.G.  is  2-1  mm2.  The  wire  will  have 
to  be  well  insulated,  as  the  voltage  per  turn  is  high. 

As  the  auto-transformer  is  only  used  for  short  times 
together,  the  induction  in  the  iron  core  can  be  as  high 
as  about  17,000  lines  per  cm2.  A  core  5  cms.  x  4, 
built,  of  course,  of  laminated  iron,  will  carry  0*3  x  106 
lines,  which  will  require  330  turns  for  220  volts. 

16's  S.W.G.,  insulated  to  0*5  mm.,  is  2'13  mm.  in 
diameter  ;  330  turns  would  make  a  coil  7*5  cms.  long 
and  2  cms.  deep.  The  iron  cores  would  be  8  cms.  long, 
the  yoke  4  cms.  high,  and  the  unwound  iron  return  in 
the  centre  5*5  cms.  wide,  all  being,  of  course,  the  5  cms. 
deep. 


APPENDIX 

EQUIVALENTS  OP  ENGLISH  AND  METRIC  MEASURES. 

1  inch  =  2*54  centimetres. 

1  square  inch  =  6 -4 5  square  centimetres. 

1  cubic  inch    =  16'39  cubic  centimetres. 

DENSITIES  OF  METALS. 

Copper  :  1  cubic  inch  weighs  O32  pound. 
Iron  :       1  cubic  inch  weighs  O28  pound. 

RESISTANCE  OP  COPPER. 

1  inch  of  copper  conductor  of  1  square  inch  area  has  a  resistance 
of  |  x  10-6  ohms  at  60°  Fahrenheit. 

1  centimetre  of  1  square  centimetre  area  =  1-7  X  10-6  ohms 
at  15°  C. 

15  per  cent,  increase  in  resistance  allows  for  a  temperature  rise 
of  about  70°  F.  or  40C  C. 


SPEEDS  OF  SYNCHRONOUS  ALTERNATING  CURRENT  MACHINES. 

POLES. 


Frequency. 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

25 
30 
40 
50 
60 
100 

1500 
1800 
2400 
3000 
3600 
6000 

750 
900 
1200 
1500 
1800 
3000 

500 
600 
800 
1000 
1200 
2000 

375 
450 
600 
750 
900 
1500 

300 
360 
480 
600 
720 
1200 

250 
300 
400 
500 
600 
1000 

214 
257 
343 
429 
514 
857 

188 
225 
300 
375 
450 
750 

167 
200 
267 
333 
400 
667 

150 
180 
240 
300 
360 
600 

136 
164 
218 
273 
327 
545 

125 
150 
200 
250 
300 
500 

114 


APPENDIX 
POLES. 


Frequency. 

26 

28 

30 

40 

50 

60 

70 

80 

90 

100 

120 

150 

25 

115 

107 

100 

75 

60 

50 

43 

38 

33 

30 

25 

20 

30 

138 

129 

120 

90 

72 

60 

51 

45 

40 

36 

30 

24 

40 

185 

171 

160 

120 

96 

80 

69 

60 

53 

48 

40 

32 

60 

231 

214 

200 

150 

120 

100 

86 

75 

67 

60 

50 

40 

60 

277 

257 

240 

180 

144 

120 

103 

90 

80 

72 

60 

48 

100 

462 

429 

400 

300 

240 

200 

171 

150 

133 

120 

100 

80 

H.-B.  CURVE  USED  IN  EXAMPLES  OF  DESIGN. 


FIG.  27. 


INDEX 


AiR-cooled  transformers,  77 
Air  space  induction,  21 
Alternators,  compound,  46 
,,  furnace,  99 

250  K.W.,  24 
,,  simple,  1 

Aluminium  as  a  conductor,  94 
Ampere,  definition  of,  5 
Ampere-turn  per  inch  diameter,  21, 

60 

Antimony  as  a  conductor,  94 
Arc-lamp,  choking  coil  for,  97 
Armature-reaction,  10 
Automatic  voltage  regulation,  48 
Auto-starter,  111 

B.-H.  CURVES,  115 
Bismuth  as  a  conductor,  94 
Brass  as  a  conductor,  94 
Bronze  as  a  conductor,  94 

CADMIUM  as  a  conductor,  94 
Capacity,  5 

Cast  iron  as  a  conductor,  94 
Cheapest  voltage  for  transmission, 

89 

Choking  coils,  96 
Compound  winding  rotaries,  76 
Compound  wound  alternators,  46 
Condensers,  5-6 
Converters,  rotary,  75 
Copper  as  a  conductor,  94,  114 
Cost  of  alternator,  89,  105 

,,       induction  motor,  70,  111 

,,       metals,  94 

,,       transformer,  84 
Coulombs,  5 
Cramp,  William,  v. 
Current,  average,  4,  6 

,,        magnetizing,  58,  84 

,,        no-load,  59 
Cyclic  irregularity,  42 


D2Z  FORMULA,  22 

Demagnetizing  A.T.'s,  17 
Densities  of  metals,  94,  114 
Depth  of  transformer  coils,  78 
Dimensions,  relative  to  output,  20 

EARLE,  H.  A.,  vi. 
Efficiency  of  alternators,  39,  105 
,,  induction  motors,  69, 

110 

Efficiency  of  transformers,  84 
E.M.F.,  production  of,  2-4 
Entz  booster,  49 
Equivalents  of  English  and  metric 

measure,  114 

FIELD,  M.B.,  26 
Frequency,  1 
Furnace  alternator,  99 

GOLD  as  a  conductor,  94 
Grime,  R.E.,  vi. 

H.-B.  CURVES,  115 
Heyland  diagram,  57 

IMPEDANCE,  5 

Induction  in  air  space,  21 

Induction  motor  theory,  51 
„      50  H.R,  61 
„      5  H.R,  106 

Inherent  regulation,  18 

Iron  as  a  conductor,  94 
„    losses,  36 

LAG,  angle  of,  8 

Lead  as  a  conductor,  94 

Leakage  flux,  stator,  12,  16 

„  „     rotor,  13,  16 

,,  ,,     in  induction  motors, 

53 
Lines,  transmission,  87 


117 


n8 


INDEX 


Load    curves    of    alternators,    35, 

104 
Loss,  iron,  36 

MAGNESIUM  as  a  conductor,  94 
Magnetizing  current  of   induction 

motor,  59 

Magnetizing     current     of     trans- 
former, 71-72 
Mercury  as  a  conductor,  94 
Motor,  induction,  theory,  51 
50  H.P.,  61 
5  H.P.,  106 
„•     synchronous,  43 

NICKEL  as  a  conductor,,  94 
No-load  current,  59 

OIL  cooling  for  transformers,  77 

PARALLEL  running  alternators,  40 
Platinum  as  a  conductor,  94 
Pole-pitch,  least,  23 
Pole-tip  thickness,  29 
Power  factor,  8,  9 

,,          ,,       zero,  36 
Price  of  metals,  94 

QUANTITY  of  electricity,  6 

KEACTANCE  voltage  of  transformers, 

73 

Eeaction,  armature,  10 
Rectifying  commutators,  47 
Regulation,     inherent,     of     alter- 
nators, 18 

Regulation  of  transformers,  72,  76 
Resistance  of  copper,  94,  114 

,,  ,,      metals,  94 

Resonance,  8 
Rotary  converters,  75 

SELF-INDUCTION,  4 

Short  circuit  current  of  alternators, 

37,  103 
ff  formula,  55 
Silver  as  a  conductor,  94 


Sine  curve,  4 

Slip  of  induction  motors,  68 

Slots  per  pole  per  phase,  25,  55,  61. 

107 

Sodium  as  a  conductor,  94 
Specific  resistances,  94 
Speeds  of  alternators,  114 
Squirrel-cage  motors,  106 
Stalloy  for  transformers,  79 
Starter,  auto,  111 
Steel  as  a  conductor,  94 
Strength,  tensile,  94 
Symbols  used,  xi. 

Synchronous  alternator  speeds,  114 
,,  motors,  43 


TANTALUM  as  a  conductor,  94 
Tensile  strength  of  metals,  94 
Tin  as  a  conductor,  94 
Total  loss  curves,  36 
Transformers,  theory,  71 

350K.W.,  81 
Transmission  lines,  87 
Tungsten  as  a  conductor,  94 
Tyrrell  regulator,  49 

VECTORS,  10 

Voltage,  cheapest  to  transmit  at, 

89 
Voltage  drop  in  alternator,  18 

,,       regulation  of  transformers, 

76 

WALKER,  MILES,  50 
Waste  field,  rotor,  16 

,,         ,,     induction  motors,  55 
Weights  of  material  of  alternator, 

39,  105 
Weights  of   material  of   induction 

motor,  70,  111 
Weights  of  material  of  transformer, 

84 
Wrought  iron  as  a  conductor,  94 

ZIGZAG  leakage  flux,  54 
Zinc  as  a  conductor,  94 


PRINTED    BY 

WILLIAM    CLOWES    AND   SONS,    LIMITED 
LONDON    AND    BECCLES 


HARPER  &  BROTHERS, 

Standard  Works  on  Electricity, 
Engineering,  &c. 


ELECTRIC  PROPULSION  OF  SHIPS. 

By  H.  M.  HOBART,  M.I.C.E. 


Demy  8vo.    44  Illustrations.    53.  net ;  post  free,  55.  4d. 

Explains  fully  the  various  systems  of  propulsion,  deals  with  such  matters  as 
"Size  and  Power,"  "Fractional  Resistance,"  "Momentum,"  "Gearing," 
"  Efficiency  of  Propellers,"  &c.,  and  shows  that  with  electrical  machinery  in  the 
equipment  a  turbine-engined  ship  can  excel  the  piston-engined  ship  both  in 
economy  and  in  manoeuvring  capacity. 


MOTOR  BODIES  AND  CHASSIS. 

By  H.  J.  BUTLER. 

With  a  Foreword  by  the  Rt.  Hon.  the  LORD  MONTAGU  OF  BEAULIEU,  Editor 
of  The  Car  Illustrated. 


Demy  8vo.    39  Illustrations.    6s.  net ;  post  free,  6s.  $d. 

A  comprehensive  work,  dealing  with  the  construction  of  the  entire  motor-car 
—bodywork    as    well    as    mechanism.      "The    Petrol    Engine,"    "Ignition," 
"Transmission,"     "Brakes,"     "Gears," 
"Upholstery,"    "Decoration,"   "Painting, 
"  Accessories,"  &c. 


Body     Design  —  various     type 
fee.,"    "Wheels,"    "Tyres,"    and 


ELECTRIC   TRAINS. 

By    H.    M.    HOBART,    M.I.C.E. 


Demy  8vo. 


With  many  Illustrations  and  Diagrams. 
6s.  net ;  post  free,  6s.  4d. 


In  view  of  the  large  amount  of  work  t®  be  done  in  the  immediate  future  in 
electrifying  extensive  sections  of  our  railways,  the  value  of  this  study  cannot  be 
over-estimated.  The  book  explains  in  a  clear,  thoroughly  practical  manner,  the 
characteristic  features  of  the  various  systems,  and  gives  abundant  material  for  the 
study  of  the  relative  merits  of  such  systems — financially  and  otherwise.  Electric  train 
manipulation  has  now  been  sufficiently  long  in  practice  to  yield  thoroughly  reliable 
data,  and  Mr.  Hobart's  conclusions  will  be  received  by  engineers  with  the  regard  due 
to  his  well-known  qualifications. 

There  are  also  chapters  devoted  to  :  Energy  Consumption  of  Trains — Influence 
of  Number  of  Stops— Influence  of  Momentum— Acceleration  and  Tractive  Force— 
Train-friction — Heating  of  Railway  Motors,  etc. 


ELEMENTS  OF  ELECTRIC  TRACTION 

FOR   MOTORMEN   AND   OTHERS. 

By  L.  W.  GANT, 

Lecturer  at  the  Leeds  Institute  Technical  School. 


Demy  8vo.     Profusely  Illustrated  by  specially  prepared  Diagrams. 
5s.  net ;  post  free,  53.  4d. 


A  work  specially  written  and  primarily  intended  for  Motormen,  Depot 
Foremen,  Inspectors,  Apprentices,  and  others  employed  on  electric  tramway 
systems  ;  to  serve  also  as  an  elementary  text-book  for  students  beginning  the  study 
of  electric  traction. 

"There  is  no  other  book  of  the  kind  and  on  the  lines  of  this  one,  in  that  the 
prevailing  central  idea  is  the  mechanism  whereby  electric  traction  is  utilized.  .  .  . 
We  have  considered  velocity,  acceleration,  load,  friction  gearing,  and  such-like 
problems,  all  of  which  bear  a  most  important  part  in  traction.  From  the  motor- 
man's  point  of  view,  and  for  immediate  application,  the  information  given  on  the 
'  Application  of  Motors  to  Traction  '  will  be  most  interesting,  although  that  about 
'  Brakes  '  will  be  almost  equally  welcomed.  Altogether  the  book  is  full  of  good 
things,  and  ought  to  be  extensively  read  and  its  contents  studied.  The  illustrative 
examples  or  proofs  to  drive  home  the  lesson  are  of  a  practical  kind." — Electrical 
Engineer. 


ELECTRIC  TRACTION. 

By  ROBERT  H.  SMITH, 

Assoc.  M.LC.E.  ;  MJ.  Mech.  E.  ;  M.LE.E.  ;  M.I.  and  St.  I. ;  Whit.  SchoL 

Demy  8vo.    465  pp.,  347  Illustrations.    Qs.  net ;  post  free,  93.  6d. 

An  up-to-date  and  authoritative  work  upon  Electric  Traction  in  all  its  aspects. 
The  dynamic  and  constructional  principles  are  dealt  with  in  detail,  and  are  mainly 
based  upon  examples  already  existing  or  actually  under  construction.  The  author 
emphasizes  the  consideration  of  economic  conditions  and  commercial  results  as 
aspects  which  call  for  more  study  than  they  generally  receive,  and  supplies  copious 
data  from  authoritative  sources. 

"  This  book  may  be  said  to  possess  a  unique  merit  in  being  a  handy  compilation 
of  facts  derived  from  practical  examples,  from  which  deductions  are  drawn  that 
may  prove  valuable  ;  .  .  .  one  of  the  best  attempts  made  to  cover  the  field." — 
Times  Engineering  Supplement. 


CONTINUOUS  CURRENT  MACHINE  DESIGN. 

By  WILLIAM  CRAMP,  M.I.E.E., 

Consulting  Engineer,  Lecturer  and  Examiner  in  Electrical  Design,  Manchester  University , 
late  Lecturer  in  Electrical  Design  at  the  Central  Technical  College,  London. 


Demy  8vo.    Profusely  Illustrated.    53.  net ;  post  free,  53.  4d. 


A  synopsis  of  the  main  points  which  arise  in  the  design  of  direct  current 
dynamos  and  motors  to  meet  various  requirements.  The  author  shows  what 
conditions  determine  the  form  and  proportions  of  machines  of  different  output, 
and  from  simple  fundamental  formulae  develops  the  main  dimensions  from  which 
the  rest  of  the  details  are  worked  out.  Practical  examples  and  complete  designs 
are  given  of  one  machine  of  each  of  the  types  discussed,  and  the  influence  upon 
cost  of  variation  in  proportions,  and  of  the  use  of  interpoles  is  shown.  The  work 
is  intended  as  a  text-book  and  guide  for  advanced  students  of  the  subject,  and  as 
a  handy  book  for  design  and  drawing  office. 


CONTINUOUS  CURRENT  ARMATURES : 

THEIR  WINDINGS   AND   CONSTRUCTION. 
By  C.  KINZBRUNNER,  A.M.I.E.E. 


Demy  8vo.     Profusely  Illustrated.    33.  6d.  net ;  post  free,  35. 


Deals  in  a  clear  and  simple  manner  with  the  methods  of  winding  continuous  current  armatures. 
Suitable  for  students,  designers,  and  workmen. 

"  Clearly  written  and  well  illustrated." — Electricity. 


TESTING  OF  CONTINUOUS  CURRENT 
MACHINES 

IN    LABORATORIES   AND   TEST   ROOMS. 
By  C.  KINZBRUNNER,  A.M.I.E.E. 


Demy  8vo.     Profusely  Illustrated.    6s.  net ;  post  free,  6s.  5d. 


Special  Chapters  are  devoted  to  :  Resistance  Measurement — Measure  of  Temperatures — 
Insulation  Measurements — Measurement  of  Speed — No-load  Characteristics — Load  Characteristics 
—Magnetic  Measurements— Efficiency— Separation  of  Losses— Practical  Testing  of  Continuous 
current  Machines. 

"Electrical  and  mechanical  engineers  will  find  instructive  data  which  may  enable  them  to 

•mount  many  a  difficulty." — Electrical  Magazine. 


surmount 


ALTERNATING  CURRENTS: 

THEIR  THEORY,  GENERATION  &  TRANSFORMATION. 
By  ALFRED  HAY,  D.Sc.,  M.I.E.E. 


Demy  8vo.    178  Illustrations  ;  307  pages.    6s.  net ;  post  free,  6s.  5d. 
Sixth  Thousand. 


CONTENTS. — Theory  of  Single-phase  and  Polyphase  Currents — Theory  of  the  Wattmeter — 
Measuring  Instruments — Alternators,  Transformers,  and  Induction  Motors — Synchronous  Motors 
and  Parallel  Running — Regulation  of  Alternators  and  Transformers — Testing  of  Alternators  and 
Transformers — Theory  of  Induction  Motors  and  Circle  Diagram — Testing  of  Induction  Motors — 
Induction  Generators  and  Speed  Control  of  Induction  Motors — Rotary  Converters — Compensated 
Induction  Motors  and  Compound  Alternators — Single-phase  Commutator  Motors. 

"  The  best  book  ever  written  on  the  subject." — Electrical  Engineer. 


ALTERNATING  CURRENT  WINDINGS : 

THEIR   THEORY  AND   CONSTRUCTION. 
By  C.  KINZBRUNNER,  A.M.I. E.E. 


Demy  8vo.    Profusely  Illustrated.    33.  6d.  net ;  post  free,  33.  gd. 


"  With  diagrams  and  photographs,  the  author  has  succeeded  in  explaining  the  various  modes 
of  winding  large  alternators  more  clearly  than  words  alone  can  possibly  do." — Electrical  Times, 


TESTING  OF  ALTERNATING  CURRENT 
MACHINES. 

GENERAL   TESTS;     TRANSFORMERS;     ALTERNATORS. 
By  C.  KINZBRUNNER,  A.M.I.E.E. 


Demy  8vo.     Profusely  Illustrated.    43.  6d.  net ;  post  free,  43.  lod. 


For  both  Electrical  and  Mechanical  Engineers  who  are  engaged  in  test-room  work,  or  in 
installing  and  supervising  electrical  machinery  ;  also  most  helpful  in  preparing  the  student  for  his 
laboratory  work. 

"  A  copy  should  be  obtained  by  every  electrical  engineer  as  a  work  of  reference." — Electrical 
Magazine. 


ELECTRICAL  ENGINEERING. 

By  Dr.  E.  ROSENBERG. 

TRANSLATED  BY 
W.  W.  H.  GEE,  A.M.I.E.E.,  AND  C.  KINZBRUNNER,  A.M.I.E.E., 

Of  the  Municipal  School  of  Technology,  Manchester. 


Demy  8vo.     Profusely  Illustrated.    6s.     i3th  Thousand. 

A  comprehensive  Text-book  for  all  who  desire  a  knowledge  of  the  chief 
principles  of  the  subject.  It  comprises,  besides  the  fundamental  phenomena 
of  the  electric  current,  dynamos,  and  motors  for  continuous,  alternating,  and 
three-phase  current,  accumulators  and  their  apparatus,  measuring  instruments, 
electric  lighting,  alternating  current  engineering,  and  polyphase  work. 

"  We  have  not  seen  any  elementary  book  on  electrical  engineering  which  is 
at  once  so  popular  and  so  practical  as  this  work." — Engineering. 

"The  author  has  accomplished  a  task  which  we  had  come  to  regard  as 
almost  impossible.  He  has  written  a  book  on  Electrical  Engineering  which  will 
enable  any  novice  to  acquire  a  clear  idea  of  the  main  principles  of  the  subject." 
—Electrical  Times. 


LABORATORY  WORK  IN  ELECTRICAL 
ENGINEERING. 

(PRELIMINARY    GRADE.) 
By  JOHN    ROBERTS,  Junr., 

Of  the  Blackburn  Technical  School. 


Demy  8vo.    Profusely  Illustrated.    53.  net ;  post  free,  55.  4d. 

Laboratory  Experiments  for  First  and  Second  Year  Students  of  Electrical  Engineer- 
ing. The  work  contains,  besides  the  usual  pure  measurements,  special  chapters  on  the 
Potentiometer,  the  Calibration  of  Electrical  Measuring  Instruments,  Dynamo  and 
Motor  Tests,  &c. 

"  This  book  is  excellent,  and  will  be  found  of  great  assistance  to  students,  and  at 
the  same  time  will  lighten  the  work  of  teacher  or  demonstrator." — Electrical  Engineer. 


THE  DISEASES  OF  ELECTRIC  MACHINERY: 

THEIR   SYMPTOMS,   CAUSES  AND    REMEDY. 
By  C.  KINZBRUNNER,  A.M.I.E.E. 


Limp  Cloth,    is.  6d.  net ;  post  free,  is.  8d.     Eighth  Thousand. 

Chapters  are  devoted  to  :  Sparking — Heating — Dynamo  fails  to  generate — Motor 
fails  to  start — Speed  of  Motor — Noise — Faults  with  Starters  and  Regulators — 
Alternating-current  Generators  with  Rotating  Armatures — Alternators  with  Rotating 
Field — Single  and  Multi-phase  Induction  Motors— The  Installation  and  Care  of 
Electric  Machines. 

"  A  book  which  might  be  placed  with  great  advantage  in  the  hands  of  an  intelligent 
mechanic  or  a  student  just  entering  the  testing  shop." — Electrician. 


PRACTICAL  ELECTRIC  WIRING 

FOR   LIGHTING   INSTALLATIONS. 
By  CHARLES  C.   METCALFE,  A.M.I.E.E., 

Electrical  Engineer  to  the  Education  Committee,  Manchester. 

Demy  8vo.     With  over  130  Illustrations  from  Original  Drawings  and 
Photographs.    55.  net  ;  post  free,  53.  4<i. 

FOURTH  THOUSAND. 


Special  Chapters  are  devoted  to:  Fitting  and  General  Arrangement — 
Tools — Accessories — Systems — Wires  and  Cables — Joints — Flexible  Conductors 
— Insulation  of  Joints — Plans  and  Schedule — Specification — Installation. 

* '  The  book  is  one  that  should  be  in  the  establishment  of  every  contractor,  if 
not  in  the  possession  of  every  wireman." — Electrical  Times. 


ELECTRIC  ARC  LAMPS: 

THEIR   PRINCIPLES,   CONSTRUCTION,  AND 
WORKING. 


By  J.    ZEIDLER, 

AND 

J.  LUSTGARTEN,  M.Sc., 

Lecturer  in  Electrical  Engineering  at  the  Municipal  School  of  Technology,  Manchester. 


Demy  8vo.    Profusely  Illustrated.    53.  net ;  post  free,  55.  4<i. 


CONTENTS.— The  Electric  Arc— The  Principles  of  Arc  Lamps— Series,  Shunt, 
and  Differential  Arc  Lamps — The  Construction  of  Arc  Lamps — Open,  Enclosed, 
and  Flame  (including  Magazine)  Arc  Lamps — Candle-power,  Light  Distribution, 
and  Application  of  Arc  Lamps  for  Lighting  Purposes — Illumination — Accessories 
for  Installation — Tables — Curves — Appendix — Comparative  Cost  of  Different 
Sources  of  Light. 


ELECTRICITY  IN  MINING. 

By  SYDNEY  F.  WALKER,  M.I.E.E.,  M.I.Min.E.,  &c. 


Demy  8vo.    Profusely  Illustrated.    93.  net ;  post  free,  93. 

mong   the  a{ 

,  water  softer 

1  combustion 

etc." — Ironmonger. 

STEAM  BOILERS,  ENGINES,  AND   TURBINES, 

AND   THEIR   ACCESSORIES. 
By  SYDNEY  F.  WALKER,  M.I.E.E.,  A.M.I.C.E.,  &c. 


Demy  8vo.     Profusely  Illustrated.    93.  net ;  post  free,  93.  5d. 

For  students,  and  for  those  engaged  in  the  use  or  manufacture  of  steam  boilers,  engines,  and 
turbines.  It  is  an  epitome  of  the  knowledge  and  practice  of  the  subject  up  to  date,  and  no  very 
advanced  mathematics  are  used. 


STARTERS  AND  REGULATORS 

FOR   ELECTRIC   MOTORS   AND   GENERATORS: 

THEORY,    CONSTRUCTION,   AND   CONNECTION. 

By  RUDOLF  KRAUSE. 

TRANSLATED  BY  C.  KINZBRUNNER  AND  N.  WEST. 


Demy  8vo.     Profusely  Illustrated.    43.  6d.  net ;  post  free,  43.  lod. 

Special  Chapters  are  devoted  to  :  Theory  of  Starters — Mechanical  Construction  of 
Starters — Calculation  of  Regulating  Resistances  for  Generators  and  Motors — Con- 
struction and  Connections  of  Regulators  for  Generators  and  Motors. 

"  Useful  to  every  one  engaged  in  the  electric  power  business,  and  no  designer  can 
afford  to  overlook  it." — Electric  Contractor. 


GERMAN    SCIENTIFIC    AND    TECHNOLOGICAL 

READER. 

BOOKS   I.   and   II. 

By  E.  CLASSEN,  B.A., 

With  the  assistance  of  J.  LUSTGARTEN,  M.Sc., 

Of  the  Manchester  School  of  Technology. 


2s.  each  net ;  post  free,  23.  sd. 

Will  enable  students  to  become  familiar  with  German  scientific  terms,  by  means  of  brief 
articles  in  German,  and  an  adequate  vocabulary. 


CONSTRUCTIONS  OF  ELECTRIC  MACHINES 
AND  APPARATUS. 

PART  I.  SWITCHBOARD  APPARATUS. 

By  C.  KINZBRUNNER,  A.M.I.E.E. 
13  in.  by  8£  in.     2s.  6d.  net ;  post  free,  2s.  gd. 

A  series  of  10  plates  showing  how  various  problems  have  been  solved. 

"The  drawings  are  very  neat,  and  doubtless  to  students  and  draughtsmen  the  plates  will  be 
very  useful  for  reference." — Electrical  Review. 

AMMONIA  AND  ITS  COMPOUNDS. 

By  J.  GROSSMANN,  M.A.,  Ph.D.,  F.I.C.,  &c. 
2s.  6d.  net ;   post  free,  2s.  gd. 

For  the  use  of  Chemists,  Engineers,  Students,  and  others  interested  in  the  manufacture  of 
chemicals,  gas,  or  coke. 

"  The  book  is  complete  and  can  be  confidently  recommended." — Dyer  and  Calico  Printer. 

HASWELL'S  ENGINEERS'  POCKET-BOOK. 

By  CHARLES   H.    HASWELL. 


Mechanics'  and  Engineers'  Pocket-Book  of  Tables,  Rules,  and 
Formulas  pertaining  to  Mechanics,  Mathematics,  and  Physics, 
including  Areas,  Squares,  Cubes  and  Roots,  etc. ;  Logarithms, 
Hydraulics,  Hydrodynamics,  Steam  and  the  Steam-Engine,  Naval 
Architecture,  Masonry,  Steam- Vessels,  Mills,  etc. ;  Limes,  Mortars, 

Cements,  etc. 


i2mo,  Leather  Pocket-Book  Form.        i8s.        i48th  Thousand. 

"  I  cannot  find  words  to  express  my  admiration  of  the  skill  and  industry  displayed  in  producing 
the  same.  To  you  belongs  the  honour  of  having  presented  to  the  world  a  book  containing  more 
positive  information  than  was  ever  before  published." — Extract  from  a  letter  from  CAPT.  J. 
ERICSSON,  the  celebrated  Engineer. 

EDISON : 

HIS   LIFE   AND   INVENTIONS. 

By  F.  L.  DYER  and  T.  C.  MARTIN  (in  collaboration  with 
Edison  himself). 


Demy  8vo.    2  Vols.    Gilt  Top.    Copiously  Illustrated.     i6s.  net. 

"  A  remarkably  interesting  picture,  not  only  of  the  life  of  one  of  the  greatest  men  of  to-day, 
but  of  the  greatest  inventive  period  in  the  history  of  the  world." — Glasgow  Herald. 

HARPER  &  BROTHERS,  45,  Albemarle  Street,  LONDON,  W. 


398921 

T7 


Engineering 
Library 

UNIVERSITY  OF  CALIFORNIA  LIBRARY 


